# Minimizing Drag Force by Adjoint Solver (RBF), ANSYS Fluent CFD Simulation Training

$242.00 Student Discount

- The problem numerically simulates the drag force on a simple cylindrical obstacle using
**ANSYS Fluent**software. - We design the 2-D model by the
**Design Modeler**software and then mesh it with**ANSYS Meshing**software. - The mesh type is
**Structured**, and the element number equals**36000**. - We aim to
**Minimize**the drag force 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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## Description

**Description**

This project is related to the numerical simulation of the **Drag** force on a simple **Cylindrical** obstacle using **Ansys Fluent** software. We aim to optimize the **Design** of this model using an **Adjoint Solver** and **Gradient-Based Optimizer**.

Such modeling 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**. In the present work, we have defined the drag force as observable.

So, the adjoint solver is based on the drag force applied to the cylinder. 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 drag force.

We use the sensitivity analysis data in the gradient-based optimizer. In this tool, we specify how the observable should be changed. For example, in this project, we consider **Decreasing** the drag force. This means changing the cylindrical geometry to **Minimize** the drag force. 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 a cylinder. For simplicity, we assumed the geometry to be two-dimensional and only modeled the circular cross-section of the cylinder.

Then we meshed the model with **Ansys Meshing** software. The mesh type is **Structured**, and the number of cells equals **36000**.

**Adjoint Solver Methodology**

We used the adjoint solver in this project to obtain the sensitivity data. For this purpose, we defined the drag force (horizontal force caused by water flow) as observable.

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 entire circular wall for deformation.

Then we created a square shape **Region** around this circular wall. We considered this square an area of â€‹â€‹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 observable changes. In this way, the drag force will **Decrease** by **thirty percent**.

We set the **Design Number** to **Ten**, so we can see a thirty percent reduction in the drag force 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.

The pressure contour shows that the highest pressure appears in front of the cylinder, as it is directly in the water flow path. The velocity contour also shows a wake behind the cylinder caused by fluid separation.

We analyzed the sensitivity in the adjoint solution. We obtained the shape sensitivity contour around the cylinder.

The highest sensitivity is shown in the upper and lower parts of the cylinder. This means that boundary displacement and shape deformation in these areas have the greatest effect on the amount of drag force.

So to reduce the drag force, we need to focus on the upper and lower parts of the geometry. In the final solution by the gradient-based optimizer, the geometry undergoes deformation.

This displacement and deformation lead to the minimization of the drag force. The drag force before optimization was equal to **2.6684692 N**. After performing the second and third steps, this force reached the value of **0.78095984 N**. So we conclude that the drag force has decreased by **70 %**.

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 **3.65042e-5 m**, and the average displacement is equal to **1.75812e-5 m**.

The comparison of designs shows that the cross-section perpendicular to the flow should be smaller to reduce the drag. So the model has partial elongation.

Finally, we can say that we achieved our goal. We reduce the drag force with the design optimization method.

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