This chapter discusses DOE Concepts and presents a general introduction to the Design of Experiments (DOE). Creating and utilizing a design of experiment (DOE) is one of the crucial and important steps in the Optimization process in ANSYS Fluent. DOE is a technique for defining sample design points to conduct experiments, so that the output variables will be obtained based on the input variables at these sample design points. DOE algorithms attempt to determine sample design points in a way that the entire space of the input parameters’ ranges is explored to obtain the output parameters. DOE is a main step before response surface methodology (RSM). So, building DOE efficiently causes improvement in the accuracy of the response surface derived from the sample design points. There are different DOE types available in ANSYS optimization. These DOE types determine the method or algorithm required to define the sample design points. These DOE types include: ّCentral Composite Design (CCD) Box-Behnken Design (BBD) Optimal Space-Filling Design (OSF) Sparse Grid Initialization Latin Hypercube Sampling Design (LHS) In CCD, there are different design types available. Including: Rotatable VIF-Optimality G-Optimality Face-Centered In OSF and LHS, there are different sample types available. Including: CCD Samples Linear Model Samples Pure Quadratic Model Samples Full Quadratic Samples

This chapter discusses RSM Concepts and presents a general introduction to the Response Surface Methodology (RSM). Response surface methodology (RSM) is one of the crucial and important steps in the Optimization process in ANSYS Fluent. RSM is a main step after the design of experiment (DOE). It means RSM utilizes results obtained from the sample design points so that it can estimate approximate values ​​throughout the design space without needing a complete solution. Note that response surfaces are functions in which the output parameters are described in terms of the input parameters. Therefore, according to the resulting values ​​at the sample design points in the range of the input parameter variations, the response surfaces can evaluate the output parameters for the entire range of the input parameter variation. There are several types of response surfaces available in ANSYS optimization. These response surface types include: ّGenetic Aggregation Full 2nd-Order Polynomials Kriging Non-Parametric Regression Neural Network Sparse Grid

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: Direct Optimization: Predicts system behavior without intermediary steps 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: Indirect Optimization: Using RSM with CCD method to generate design points and perform parameter correlation analysis 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 Input Parameters Range Output Parameters Cone angular velocity 100-400 rad/s Outlet temperature Outer diameter 0.099-0.121 m CO₂ mass fraction Cone height 0.027-0.033 m CO mass fraction Cone length 0.27-0.33 m Average temperature Air inlet diameter 0.0018-0.0022 m Total heat generation Fuel inlet diameter 0.009-0.011 m Chamber heat flux Air inlet offset 0.009-0.011 m   Fuel inlet offset 0.009-0.011 m   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: Boundary Type Settings Air Inlet Mass flow inlet 0.00036135 kg/s, 300 K Fuel Inlet Mass flow inlet 3 kg/s, 300 K Outlet Pressure outlet - Chamber walls Stationary wall Convection: h=25 W/m²K, T∞=300 K Cone Rotating wall Angular velocity (input parameter), Adiabatic 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.

Project Overview A high-speed compressor cascade wind tunnel is utilized to investigate secondary flow phenomena in the corner and sidewall regions of axial compressors. This project focuses on optimizing a compressor cascade using the Multi-Objective Genetic Algorithm (MOGA) method. Initially, we simulated a sectional compressor cascade configuration. Subsequently, we performed optimization involving three input parameters and two output parameters. The input parameters include inlet velocity (v_in), angle of attack (alpha_degree), and pitch. The output parameters are drag force and lift force. The objective function is defined to minimize drag force toward zero, maximize lift force to 0.07, and achieve a beta angle of -12 degrees. Geometry and Meshing The geometry was created as a 3D model using DesignModeler software. A computational grid was generated using ANSYS Meshing software, featuring an unstructured mesh with tetrahedral cells and 5 boundary layers. The total mesh contains 991,872 cells. Optimization Methodology All optimization procedures were executed in ANSYS Workbench software using Multi-Objective Genetic Algorithm (MOGA). The Box-Behnken Design (BBD) method was implemented for the Design of Experiments (DOE) stage, while Genetic Aggregation served as the Response Surface Method (RSM). The input parameter ranges are defined as follows: Inlet velocity: 3 to 30 m/s Pitch: 1 to 7 mm Angle of Attack: -10° to +10° Results and Analysis Results were obtained at each of the three main optimization stages for analysis and optimal point selection. A summary table presents the design points and their corresponding execution results. ANSYS Workbench utilized the DOE results to generate response surfaces for predictive analysis. Sensitivity charts illustrate how output parameters respond to variations in input parameters. The analysis reveals that all three input parameters positively influence lift force, with velocity demonstrating the strongest effect. While velocity positively affects both lift and drag forces, it negatively influences the beta angle. Conversely, pitch exhibits the most significant impact on the beta angle. Optimization Outcomes Upon completion of the optimization process, ANSYS Workbench identified three candidate points as optimal solutions, along with three verification points for validation.

In this project, we present the optimization process of a solar chimney using the Design of Experiments (DOE) in ANSYS software. We intend to optimize the design of a solar chimney. Therefore, we defined 3 input parameters (geometric factors), including tower height, collector radius, and the angle of the absorber plate. Then, we defined the airflow rate as the target output parameter. 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 Optimal Space-Filling Design (OSPF). According to the maximum and minimum ranges for all three input parameters, 15 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. Solar Chimney Optimization using Design of Experiments (DOE) in ANSYS Project Overview This project demonstrates the optimization of a solar chimney using Design of Experiments (DOE) methodology in ANSYS software. A solar chimney comprises a tall vertical tower connected to a wide circular collector at its center. Air enters through a gap between the ground and the collector’s absorber plates surrounding the chimney base, while the outlet is located at the tower’s top. Solar radiation on the absorber plate transfers heat to the airflow beneath the collector. Rising air temperature causes decreased air density and pressure, making buoyancy effects dominant. Consequently, air moves upward at significant velocity. Methodology Geometry and Meshing: The 3D solar chimney with simplified construction was modeled in Design Modeler software, followed by mesh generation in ANSYS Meshing software. Optimization Parameters: The optimization process focuses on three input parameters (geometric factors): Tower height Collector radius Absorber plate angle The target output parameter is airflow rate. Optimization Process: The Design Exploration tool was employed for optimization through two stages: Design of Experiments (DOE): Design points were generated using Optimal Space-Filling Design (OSFD). Based on maximum and minimum ranges for all three input parameters, 15 design points were created. Response Surface Methodology (RSM): Output parameter values were estimated using Genetic Aggregation algorithms. Results and Analysis Parameter Effects: RSM-generated 2D and 3D plots of mass flow rate reveal the simultaneous effects of the three input parameters. Results demonstrate that increasing tower height, collector radius, and absorber plate angle all increase mass flow rate. Tower Height Impact: As tower height increases, the pressure difference between base and top increases (ΔP = ρgh). This greater pressure differential enhances buoyancy force, accelerating upward hot air movement. Collector Radius Impact: Increasing collector radius expands the collector area, enabling greater solar absorption and enhanced heat transfer to air beneath the collector. Higher temperatures reduce air density, strengthening buoyancy forces. Absorber Plate Angle Impact: Increasing the collector’s slope creates a greater suction effect, facilitating easier hot airflow movement toward the chimney. Optimal Design: The optimal configuration is achieved at maximum values for height, radius, and angle. Comparison between baseline and optimal cases was performed using velocity contours and vectors. Validation and Sensitivity: Additional analysis included: Local Sensitivity Plots: Quantifying each input parameter’s influence on the output parameter Goodness of Fit Plots: Assessing the accuracy of RSM-estimated results compared to actual design point results, confirming the reliability of the optimization process

In this project, we present the optimization process for improving the thermal performance of a microchannel heat sink using the Design of Experiment (DOE) in ANSYS software. We intend to optimize the design of a microchannel heat sink. Therefore, we defined 3 input parameters: Two geometric factors, including the length and height sizes of the rectangular cross-section of the cooling fluid channel, and one operating factor, i.e., porosity of the porous medium of the channel. Then, we defined the maximum temperature of the microchannel surface as the target output parameter. 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 Latin Hypercube Sampling Design (LHSD). According to the maximum and minimum ranges for all three input parameters, 10 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. Microchannel Heat Sink Thermal Performance Optimization using Design of Experiments (DOE) in ANSYS Project Overview This project presents the optimization process for enhancing the thermal performance of a microchannel heat sink using Design of Experiments (DOE) methodology in ANSYS software. Microchannel heat sinks are effective devices for dissipating substantial heat generated by high-power electronic components. Their widespread application stems from high heat transfer coefficients and large specific surface areas. The modeled microchannel heat sink features a solid body containing a cooling fluid channel filled with porous media. While typical microchannel heat sinks comprise multiple channel rows, this model represents a single microchannel section for computational simplicity. Methodology Geometry and Meshing: The 3D microchannel heat sink was modeled in Design Modeler software, with subsequent mesh generation performed in ANSYS Meshing software. Optimization Parameters: The optimization process incorporates three input parameters: Geometric Factors (2): Length and height dimensions of the rectangular cooling fluid channel cross-section Operating Factor (1): Porosity of the porous medium within the channel The target output parameter is the maximum temperature on the microchannel surface. Optimization Process: The Design Exploration tool facilitated optimization through two sequential stages: Design of Experiments (DOE): Design points were generated using Latin Hypercube Sampling Design (LHSD). Based on defined maximum and minimum ranges for all three input parameters, 10 design points were created. Response Surface Methodology (RSM): Output parameter values were estimated using Genetic Aggregation algorithms. Results and Analysis Parameter Effects: RSM-generated 2D and 3D plots of maximum temperature illustrate the combined effects of the three input parameters. Results demonstrate that increasing length, height, and porosity all decrease maximum temperature. Channel Dimension Impact: Increasing the cooling channel’s length and height reduces the heat sink surface’s maximum temperature. Larger length and height dimensions expand the cooling channel cross-section, increasing incoming fluid flow rate. This enhancement improves heat transfer and cooling efficiency. Porosity Impact: Increasing porous medium porosity within the cooling channel reduces the heat sink’s maximum temperature by enhancing heat transfer processes. However, porosity effects on surface temperature are less pronounced than geometric parameters (length and height). Validation and Sensitivity: Additional analysis included: Local Sensitivity Plots: Quantifying each input parameter’s influence on the output parameter, revealing the relative importance of geometric versus operating parameters Goodness of Fit Plots: Validating the accuracy of RSM-estimated results against actual design point results, confirming the optimization methodology’s reliability Key Finding: The optimal thermal performance is achieved by maximizing channel dimensions (length and height) and porosity, with geometric parameters demonstrating stronger influence on cooling performance than porosity variations.