By Laura Trappolini
The question is whether to mesh or not to mesh.
If Hamlet from Shakespeare were a computational fluid dynamics (CFD) engineer in the twenty-first century, that would likely be the updated version of his existential query. The original Hamlet, prompted by the death of a close relative, muses on the pros and cons of existence and considers the issue “To be or not to be,” which centers on whether life is better or worse. Furthermore, considering the current state of CFD technology and the emergence of meshless technology, one may ask:
Will the mesh-based finite volume CFD approach eventually be rendered obsolete by Smoothed Particle Hydrodynamics (SPH)? And which is superior to the other? The “to be or not to be” dilemma is still unsolvable, according to the original Hamlet’s conclusion. He cannot decide whether or not to be on either side because there is no assurance that either side—alive or dead—is superior to the other. Philosophy aside, let’s get back to fluid dynamics. Does the revised CFD dilemma, “To mesh, or not to mesh,” still remain unanswerable? Is there no assurance that the meshless technology or the mesh-based approach is superior to the other? In this post, we’ll attempt to address that query.
The use of numerical simulation is becoming more and more common in the solution of many fluid dynamics-related applications. In recent years, two methods have developed simultaneously.
The late 1960s saw the emergence of eulerian approaches. These methods rely on fixed, movable, or geometric grids. Flow characteristics, such as pressure or velocity, are calculated at every mesh cell using numerical formulations like finite volumes, finite differences, or finite elements. Today, the majority of fluid applications are highly successful with the finite volume approaches.
However, there are certain situations where using mesh-based approaches presents challenges, especially when dealing with massive deformations, complicated moving objects, or highly dynamic free surface flows. And although finite volume technologies of today can overcome those, this usually comes at an additional computational cost.
Gingold, Monaghan, and Lucy (1977) developed the so-called Smoothed-Particle Hydrodynamics (SPH) method as a Lagrangian approach to address and overcome these limitations. This technology is a component of a new wave of numerical techniques that were created to get beyond meshing-related limitations.
The SPH meshless approach, which is still based on the Navier-Stokes equations, uses moving elementary bodies, or particles, to simulate fluid flow. Thus, the continuous space domain is discretized by moving particles. This outlines a technique based on particles.
Each of the particles is tracked independently, with a unique size, velocity, and position. They carry the state variables of the fluid parcel (velocity, density, pressure, temperature, etc.), just like mesh cells in conventional finite-volume approaches. Using a kernel function, this evaluation takes into account the contribution of the adjacent particles, providing the formulation’s smoothing characteristic.
Even when two solid entities come into contact, the SPH meshless approach can readily adapt to complicated moving objects since it is Lagrangian in nature. Despite the presence of numerous jets and splashes in the fluid flow, the SPH technology portrays the free surface between liquid and gas with negligible diffusivity, even if it does not discretize the gas phase.
The numerical features of accuracy and stability have been the subject of numerous research recently (Groenenboom et al., 2019; Shadloo et al., 2016; Violeau and Rogers, 2016). The current industrial use of the SPH solver for industrial applications in several fluid mechanic sectors, including the automotive, marine, and aerospace industries, is made possible by research and development.
The good news is that we will combine these two streams of historical CFD methodologies into a single CFD software solution with the introduction of Simcenter STAR-CCM+ 2402. Depending on your needs for accuracy vs. speed, you can now select, for an initial set of applications, between mesh-free SPH CFD and mesh-based finite volume SPH CFD with the SPH add-on license.
Compared to previous multiphase models, the SPH process in Simcenter STAR-CCM+ offers a seamless user experience because the volume meshing stage is eliminated. It makes use of Simcenter STAR-CCM+’s sophisticated 3D CAD pre-processing, just like mesh-based methods do. However, to further increase productivity, SPH can fully handle non-closed or non-conformal geometries, unlike standard finite volume approaches. Furthermore, even in the case of solid-body contacts, such as those between the teeth of rotating gears, the SPH model reliably reproduces complicated motions.
For such a powertrain gearbox, the typical objective is to minimize the volume of oil inside the casing of the gearbox while ensuring the oil gets into critical locations. Ideally, we would like to minimize the churning losses of the machine and therefore, optimize its efficiency. As you can see in the animation, you can seamlessly leverage the unrivaled power of Simcenter STAR-CCM+ visual post-processing and look at where the fluid goes by visualizing the particles and monitoring wall wetting.
However, you can also take advantage of all the quantitative data analytics features offered by Simcenter STAR-CCM+, and in this particular case, limit the churning losses by observing how forces and torque change over the course of your simulation.
In terms of performance, a gearbox simulation with 0.5 million particles may be completed on eight CPUs in about an hour thanks to SPH in Simcenter STAR-CCM+ version 2402. You may even examine a gearbox in an amazing duration of just 12 minutes by running the same job on 64 CPUs, showcasing the solver’s exceptional scalability. Moreover, SPH practically eliminates preparation time, allowing for quick CFD-driven insights.
The ability to automatically search and choose hidden items within a particular assembly or throughout the full 3D environment is made possible by the new command, choose Invisible. When hidden objects are discovered, visible objects remain visible and any hidden objects are shown in the 3D View window. For the best view, you’ll be prompted to switch to Translucent Shell highlight selection mode. You may see hidden parts clearly, analyze them, and take out superfluous sections for the perspective of the 3D illustration while keeping the context of the entire assembly for catalogs and other technical publications, thanks to automatic search and the new highlight selection mode.
Returning to the primary issues of powertrain design, you can easily determine whether oil reaches vital spots and reduce churning losses by utilizing the state-of-the-art SPH technology found in Simcenter STAR-CCM+ version 2402. You can simulate and evaluate complex CFD simulations more quickly and early in the development cycle with the SPH add-on license.
You will be able to choose the ideal design and conditions using the Design Manager because of the optimized workflow. Additionally, you can stay integrated in a single-user environment and conduct more in-depth simulations using the FEA solver or VOF liquid/air computations.
We compared setup engineering time between finite-volume and SPH approaches for gearbox lubrication applications.
In terms of engineering time required to set up the simulation, there is no denying that the SPH workflow is quicker than the finite-volume method. Simply said, you can avoid the volume meshing stage and other complicated procedures like overset when using SPH meshless technology to adjust the rotation speed of each gear.
For a sophisticated industrial gearbox, setting up the motion and volume mesh can sometimes take several weeks. You can simply omit that complicated step from an SPH computation.
With SPH, you can solve your most complicated applications with speed and plausibility using a low-fidelity solution. When using finite-volume methods, obtaining an initial low-fidelity solution typically requires going back to your setup and making minor adjustments to the mesh and/or numerical settings. To get over meshing-related limitations, the SPH meshless technology is a supplement to conventional finite-volume multiphase models now in use.
SPH is the ideal solver for design exploration to eliminate quickly and effortlessly low-performance design. Now, if you need to model the influence of the air or if you need to model phase change or other complex phenomena such as electromagnetics, you must use finite-volume methods. It all depends on the scope of your applications and the required level of fidelity to make that choice.
