Maximizing Lift to Drag Ratio by Adjoint Solver (RBF), ANSYS Fluent CFD Simulation Tutorial
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- The problem numerically simulates lift to drag ratio on an airfoil using ANSYS Fluent software.
- We design the 2-D model by the Design Modeler software.
- We mesh the model with ANSYS Meshing software, and the element number equals 207521.
- We aim to Maximize the lift to drag ratio in a three-step simulation.
- We use the Adjoint Solver to analyze the Shape Sensitivity.
- The Design Optimization is performed with the Gradient-based Optimizer.
- We use the Radial Basis Function (RBF) to apply Mesh Morphing.
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This project is related to the numerical simulation of the Lift to Drag Ratio on an Airfoil using Ansys Fluent software. We aim to optimize the Design of this model using an Adjoint Solver and Gradient-Based Optimizer.
Investigating the performance of airfoils is one of the most popular issues in aerodynamics for engineers and designers. Optimal design is very important in aerodynamic performance.
Two important aerodynamic forces include drag and lift. The drag force is applied in the direction of the flow, and the lift force is perpendicular to the flow.
Since the drag force is against the direction of airfoil movement, it reduces its acceleration. Since the lift force is upward, it is a positive factor in overcoming the weight force.
So reducing the drag force and increasing the lift force improves the performance of the airfoil. Consequently, in this problem, we aim to increase the lift-to-drag ratio.
This simulation is done in Three stages. First, we perform the conventional flow simulation. In the second step, we analyze the Sensitivity with the adjoint solver. Finally, we change the model’s design to achieve Optimal performance with the gradient-based optimizer.
The adjoint solver provides a series of data that is expressed in the form of sensitivity analysis. We focus on Shape sensitivity.
This tool identifies which areas of the geometry have the greatest influence on system performance.
So we need to define a target parameter. This output parameter is called Observable. If we want to define a combination of observables, we must use an Operation. In the present work, we have defined lift to drag ratio as an operation.
The adjoint solver is based on lift to drag ratio applied to the airfoil. Wherever more sensitivity is shown, i.e., Displacement of the boundary or Deformation of the shape of the design, it has a greater effect on the lift to drag ratio.
We use the sensitivity analysis data in the gradient-based optimizer. In this tool, we specify how the operation should be changed. For example, in this project, we consider Increasing the lift to drag ratio. This means changing the airfoil geometry to Maximize the ratio. These changes should lead to an optimal design.
We modeled the geometry of the project using Design Modeler software. This model is the computational zone around an airfoil.
Then we meshed the model with Ansys Meshing software. The model mesh is unstructured, and the number of cells is equal to 207521.
Adjoint Solver Methodology
We used the adjoint solver in this project to obtain the sensitive data. For this purpose, we defined the lift-to-drag ratio as operation.
We then used the sensitivity data to solve the gradient-based optimizer. Before solving the gradient-based optimizer, we performed some settings in the Design Tool tab.
In the section of the zone to be modified, we determined the airfoil wall for deformation.
Then we created a rectangle shape Region around this airfoil. We considered this rectangle an area of the domain where geometry and mesh changes are supposed to occur.
When the shape is deformed, and its boundaries are moved, the mesh around this area changes.
To apply mesh changes, we used the Mesh Morphing technique. There are three methods for mesh morphing: polynomial, direct interpolation, and Radial Basis Functions (RBF).
In this project, we used RBF for mesh morphing. For the radial basis function, the mesh deformation is interpolated from the control points.
In the Objective part, we determined the value of operation changes. In this way, the lift-to-drag ratio will Increase by 0.05 %.
We set the Design Number to Ten, so we can see a 0.05 % reduction in the ratio in the ten stages.
Adjoint Solver Conclusion
As we said, the present simulation is done in three consecutive steps. So we investigated the results in three steps.
In conventional flow simulation, we obtained velocity and pressure contours. These contours showed the distribution of velocity and pressure inside the domain.
We analyzed the sensitivity in the adjoint solution. We obtained the shape sensitivity contour around the airfoil.
The highest sensitivity is shown at the trailing edge of the airfoil. This means that boundary displacement and shape deformation in these areas have the greatest effect on the amount of lift to drag ratio.
So to increase the ratio, we need to focus on the airfoil’s trailing edge. In the final solution by the gradient-based optimizer, the geometry undergoes deformation.
This displacement and deformation lead to the maximization of the ratio. The lift-to-drag ratio before optimization was equal to 0.34677032. After performing the second and third steps, this ratio reached the value of 2.0979013. So we conclude that the lift-to-drag ratio has increased by 83 %.
Also, we displayed the graph of the location of different points in two states: initial and optimal design. We can see the shape deformation and boundary displacement. The maximum boundary displacement is equal to 1.68049e-4 m, and the average displacement is equal to 1.90683e-5 m.
Finally, we can say that we achieved our goal, and the lift-to-drag ratio was increased with the design optimization method.
This CFD Project is the 3th episode of the RBF Morph (Mesh Morphing) Training Course.