Minimizing Pressure Drop by Adjoint Solver (RBF), ANSYS Fluent CFD Simulation Training

Description

Description

This project is related to the numerical simulation of the Pressure Drop in a tube with a U-shaped bend 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 pressure drop as observable.

So, the adjoint solver is based on the pressure drop in the tube. 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 pressure drop.

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 pressure drop. This means changing the pipe geometry to Minimize the pressure drop. 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 inside a tube with a U-shaped bend.

Then we meshed the model with Ansys Meshing software. The model mesh is Structured, and the number of cells is equal to 26400.

Adjoint Solver Methodology

We used the adjoint solver in this project to obtain the sensitivity data. For this purpose, we defined the pressure drop (pressure difference between inlet and outlet) 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 only determined the inner wall of the tube for deformation.

Then we created a rectangle shape Region in the vicinity of the pipe bend. We considered this square 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 observable changes. In this way, the pressure drop will Decrease by 3 %.

We set the Design Number to Ten, so we can see a 3 % reduction in the pressure drop 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 fluid flow experiences a pressure drop after passing through the pipe bend.

We analyzed the sensitivity in the adjoint solution. We obtained the shape sensitivity contour inside the tube.

The highest sensitivity is shown in the vicinity of the pipe bend. This means that boundary displacement and shape deformation in these areas have the greatest effect on the value of pressure drop.

So to reduce the pressure drop, we need to focus on bend 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 pressure drop. The pressure drop before optimization was equal to 13.228147 Pa. After performing the second and third steps, this pressure drop reached the value of 8.1441545 Pa. So we conclude that the pressure drop has decreased by 38 %.

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 8.95115e-7 m, and the average displacement is equal to 3.37765e-7 m.

Finally, we can say that we achieved our goal, and the pressure drop was reduced with the design optimization method.

This CFD Project is the 4th episode of the RBF Morph (Mesh Morphing) Training Course.