R. Pasolari
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VPMFoam
A 2D Incompressible Hybrid Eulerian-Lagrangian Solver for External Aerodynamics
A common requirement across these diverse fields is the need for an in-depth understanding of aerodynamics. Accurate aerodynamic analysis is essential for enhancing design, efficiency, and effectiveness. However, the fast-paced nature of modern advancements limits reliance on experimental methods alone, as these can be time-consuming, costly, and impractical for all possible configurations. Consequently, combining experimental and computational studies becomes crucial.
This is where Computational Fluid Dynamics (CFD) comes into play. The development of efficient and accurate CFD tools has become essential in scientists' and engineers' hands to explore aerodynamics quickly and understand the physics of the flows. This fact has driven the present research. The primary goal of this dissertation is the development of a computational tool that is both accurate and efficient for exploring external aerodynamics simulations.
The main approaches in CFD today are the Eulerian and Lagrangian approaches, each comprising a family of methods. Eulerian methods, like the Finite Volume Method (FVM) and Finite Element Method (FEM), have been extensively used in exploring external aerodynamics, with their greatest advantage being accuracy in capturing the boundary layers. However, due to the diffusive nature of these methods, artificial diffusion is introduced into the flow, damping the vortex structures, which are crucial in many applications driven by strong body-vortex interactions. Moreover, the study of multibody objects often requires special treatments, especially for mesh generation, making the simulations extremely costly.
On the other hand, Lagrangian methods, like the Vortex Particle Method (VPM), are excellent for studying flows with a high presence of vortices, as they can preserve the vortex structures without damping them. Additionally, the particles participating in the flow are self-adaptive, satisfy the far-field boundary conditions automatically, and allow for easy implementation of multiple bodies into the simulation. However, resolving the boundary layer is very challenging and often very costly due to the inability to use anisotropic elements, making them less ideal for predicting aerodynamic forces.
Lagrangian solvers have become very popular in the last two to three decades, primarily due to the significant advancements in computer hardware, especially GPUs, which enable very fast calculations. This has encouraged engineers to explore ways to leverage this advantage in CFD, leading to the development of hybrid solvers that couple Eulerian and Lagrangian solvers. In this coupled approach, Eulerian solvers can be applied near the solid body to accurately and efficiently resolve the boundary layer region, while Lagrangian solvers preserve the vortex structures further from the body.
Building on this approach, this dissertation introduces a hybrid Eulerian-Lagrangian solver, named VPMFoam, developed to combine the strengths of both methods while minimizing their limitations. This is achieved by integrating OpenFOAM, a widely used open-source CFD software, with a Lagrangian VPM. The primary goal is to create an accurate tool focused on external aerodynamics that can efficiently handle cases with strong body-vortex interactions and multibody scenarios while maintaining a lower computational cost compared to pure Eulerian solvers. OpenFOAM was chosen primarily for its open-source flexibility and its extensive user base in academia and industry, offering broad access to this tool.
The solver's development focuses on a 2D version, with validation conducted through a step-by-step approach, starting with simple cases that exclude solid bodies. Once the successful coupling of the two solvers is verified, validation proceeds with cases involving solid bodies, such as flow around a cylinder. In these cases, the solver accurately predicts fluid flow and aerodynamic coefficients, showing strong agreement with established Eulerian solvers and effectively preserving the vorticity field in the wake. Further validations address dynamic mesh motions and multibody applications.
Following validation, the solver is applied to more realistic scenarios, including the static and dynamic stall of an airfoil and the simulation of hybrid Vertical Axis Wind Turbines using actuator models. A performance analysis of the code’s efficiency is also presented, highlighting the solver’s capability to conduct fast and accurate simulations.
By effectively combining the strengths of both Eulerian and Lagrangian approaches, VPMFoam addresses key challenges in aerodynamic analysis, particularly in cases with strong body-vortex interactions, and lays a strong foundation for further applications, including potential 3D extensions. This makes VPMFoam a valuable asset for applications requiring both high fidelity and computational efficiency. ...
A common requirement across these diverse fields is the need for an in-depth understanding of aerodynamics. Accurate aerodynamic analysis is essential for enhancing design, efficiency, and effectiveness. However, the fast-paced nature of modern advancements limits reliance on experimental methods alone, as these can be time-consuming, costly, and impractical for all possible configurations. Consequently, combining experimental and computational studies becomes crucial.
This is where Computational Fluid Dynamics (CFD) comes into play. The development of efficient and accurate CFD tools has become essential in scientists' and engineers' hands to explore aerodynamics quickly and understand the physics of the flows. This fact has driven the present research. The primary goal of this dissertation is the development of a computational tool that is both accurate and efficient for exploring external aerodynamics simulations.
The main approaches in CFD today are the Eulerian and Lagrangian approaches, each comprising a family of methods. Eulerian methods, like the Finite Volume Method (FVM) and Finite Element Method (FEM), have been extensively used in exploring external aerodynamics, with their greatest advantage being accuracy in capturing the boundary layers. However, due to the diffusive nature of these methods, artificial diffusion is introduced into the flow, damping the vortex structures, which are crucial in many applications driven by strong body-vortex interactions. Moreover, the study of multibody objects often requires special treatments, especially for mesh generation, making the simulations extremely costly.
On the other hand, Lagrangian methods, like the Vortex Particle Method (VPM), are excellent for studying flows with a high presence of vortices, as they can preserve the vortex structures without damping them. Additionally, the particles participating in the flow are self-adaptive, satisfy the far-field boundary conditions automatically, and allow for easy implementation of multiple bodies into the simulation. However, resolving the boundary layer is very challenging and often very costly due to the inability to use anisotropic elements, making them less ideal for predicting aerodynamic forces.
Lagrangian solvers have become very popular in the last two to three decades, primarily due to the significant advancements in computer hardware, especially GPUs, which enable very fast calculations. This has encouraged engineers to explore ways to leverage this advantage in CFD, leading to the development of hybrid solvers that couple Eulerian and Lagrangian solvers. In this coupled approach, Eulerian solvers can be applied near the solid body to accurately and efficiently resolve the boundary layer region, while Lagrangian solvers preserve the vortex structures further from the body.
Building on this approach, this dissertation introduces a hybrid Eulerian-Lagrangian solver, named VPMFoam, developed to combine the strengths of both methods while minimizing their limitations. This is achieved by integrating OpenFOAM, a widely used open-source CFD software, with a Lagrangian VPM. The primary goal is to create an accurate tool focused on external aerodynamics that can efficiently handle cases with strong body-vortex interactions and multibody scenarios while maintaining a lower computational cost compared to pure Eulerian solvers. OpenFOAM was chosen primarily for its open-source flexibility and its extensive user base in academia and industry, offering broad access to this tool.
The solver's development focuses on a 2D version, with validation conducted through a step-by-step approach, starting with simple cases that exclude solid bodies. Once the successful coupling of the two solvers is verified, validation proceeds with cases involving solid bodies, such as flow around a cylinder. In these cases, the solver accurately predicts fluid flow and aerodynamic coefficients, showing strong agreement with established Eulerian solvers and effectively preserving the vorticity field in the wake. Further validations address dynamic mesh motions and multibody applications.
Following validation, the solver is applied to more realistic scenarios, including the static and dynamic stall of an airfoil and the simulation of hybrid Vertical Axis Wind Turbines using actuator models. A performance analysis of the code’s efficiency is also presented, highlighting the solver’s capability to conduct fast and accurate simulations.
By effectively combining the strengths of both Eulerian and Lagrangian approaches, VPMFoam addresses key challenges in aerodynamic analysis, particularly in cases with strong body-vortex interactions, and lays a strong foundation for further applications, including potential 3D extensions. This makes VPMFoam a valuable asset for applications requiring both high fidelity and computational efficiency.
Computational efficiency of vortex particle methods (VPMs) is hindered by the particle count increasing in simulation time. To reduce the number of computational elements, two algorithms are presented that downsample the discretized vorticity field representation in two-dimensional variable-core-size VPMs. The two methods are based on existing schemes of particle merging and regridding, and are adapted to follow a compression parameter set a priori. The effectiveness of the schemes is demonstrated on two benchmark cases of external flow: A stationary Lamb-Oseen vortex and an advecting vortex dipole. In both cases, compression is associated with a drastic reduction in particle count and computation time at a cost of diffusive errors in the vorticity field. Crucially, for gentle compression steps applied at appropriate intervals, the immediate errors in the vorticity field are comparable to reference cases despite great improvements in computational time. To examine the long-term impact of compression on accuracy and performance, it is recommended that repeated compressive steps be tested on more complex cases of bluff-body wakes, with a focus on the impact of downsampling on surface forces.
Hybrid Eulerian–Lagrangian solvers have gained increasing attention in the field of external aerodynamics, particularly when dealing with strong body–vortex interactions. This approach effectively combines the strengths of the Eulerian component, which accurately resolves boundary layer phenomena, and the Lagrangian component, which efficiently evolves the wake downstream. This study builds on our team's previous work by enhancing the capabilities of a two-dimensional hybrid Eulerian–Lagrangian solver. We aim to upgrade our solver which was initially designed for static cases, to now also simulate cases involving moving objects. To ensure the reliability and applicability of a new solver, it is essential to validate its performance in complex cases. Here, the solver is validated across the case of a traveling cylinder and the case of a rotating cylinder in two different rotational speeds at low Reynolds numbers. In the realm of Eulerian solvers, such as OpenFOAM (utilized for the Eulerian component of this hybrid approach), traditional techniques include the use of morphing meshes, overset meshes, and Arbitrary Mesh Interfaces (AMI) to model body motion. The proposed methodology involves extending the Eulerian mesh up to a short distance from the solid boundary and moving it entirely as a solid entity. Then the Lagrangian solver is responsible for calculating the updated boundary conditions, thereby completing the hybrid solver's functionality. This approach is very similar to the overset mesh technique. However, unlike the traditional method where an Eulerian mesh moves on top of a static one, our method involves the motion of an Eulerian mesh over a Lagrangian grid. We compared the results from our hybrid solver with those from a purely Eulerian solver, specifically OpenFOAM. The comparison demonstrates that our solver can replicate OpenFOAM's results with high accuracy. Another interesting point highlighted in this study is the presence of high-frequency oscillations in the body forces in hybrid solvers that incorporate the redistribution of Lagrangian particles and do not utilize surface elements such as vortex panels, specifically when dealing with dynamic mesh simulations. When the Eulerian mesh travels on top of the Lagrangian grid of particles, the positions of the particles with respect to the Eulerian mesh continuously change. This results in a constant shift of particles near the solid body, where the highest vorticity is observed. Particles that are close to the solid boundary at one time step may find themselves inside the boundary at the next time step, leading to their removal. This pattern continuously changes during the simulation, causing fluctuations in the boundary conditions of the Eulerian solver and manifesting as oscillations in the forces acting on the body. It is shown that this issue can be alleviated either by increasing the spatial resolution of the Lagrangian solver or by synchronizing the movement of the Lagrangian grid with the motion of the Eulerian mesh. The results of the study make the solver trustworthy and pave the way for more demanding external aerodynamic simulations.
The past few decades have witnessed a growing popularity in Eulerian–Lagrangian solvers due to their significant potential for simulating aerodynamic flows, particularly in cases involving strong body–vortex interactions. In this hybrid approach, the two component solvers are mutually coupled in a two-way fashion. Initially, the Lagrangian solver can supply boundary conditions to the Eulerian solver, while the Eulerian solver functions as a corrector for the Lagrangian solution in regions where the latter cannot achieve high accuracy. To utilize such tools effectively, it is vital for them to be capable of handling dynamic mesh movements. This study builds upon the previous research conducted by our team and extends the capabilities of the hybrid solver to handle dynamic meshes. While OpenFOAM, the Eulerian component of this hybrid code, incorporates built-in dynamic mesh properties, certain modifications are necessary to ensure its compatibility with the Lagrangian solver. More specifically, the evolution algorithm of the pimpleFOAM solver needs to be divided into two discrete steps: first, updating the mesh, and later, evolving the solution. This division enables a proper coupling between pimpleFOAM and the Lagrangian solver as an intermediate step. Therefore, the primary objective of this specific paper is to adapt the OpenFOAM solver to meet the demands of the hybrid solver and subsequently validate that the hybrid solver can effectively address dynamic mesh challenges using this approach. This approach introduces a pioneering method for conducting dynamic mesh simulations within the OpenFOAM framework, showcasing its potential for broader applications. To validate the approach, various test cases involving dynamic mesh movements are employed. Specifically, all these cases employ the Lamb–Oseen diffusing vortex, but each case incorporates different types of mesh movements, including translational, rotational, oscillational, and combinations thereof. The results from these cases demonstrate the effectiveness of the proposed OpenFOAM algorithm, with the maximum relative errors —when compared to the analytical solution across all presented cases—capped at (Formula presented.) for the worst-case scenario. This affirms the algorithm’s capability to successfully handle dynamic mesh simulations with the proposed solver.