Piston Bowl Design Optimization and Meshing for CFD

Figure 1: Automatic structured multiblock grid generation for piston bowl design variants in a parametric optimization loop.

1739 words / 9 minutes read

Introduction

The past decade has witnessed a r[EV]olution of electric cars. Every carmaker has taken up the electric fight to the factory floor either in a small or a big way. The threat for diesel engines is not only from the new technology but also from government taxes, increasing fuel prices, and a push for cleaner mobility. The threats are more real than ever with companies like Tesla, Rivian, etc. making it an existential threat. However, the curtains are not down for the gasoline/diesel engines, “10 years from now, 80 percent of the cars on the road worldwide will still use gasoline or diesel engines.”, says Barb Samardzich, Ford’s vice president for powertrain engineering. Electric or gasoline/diesel in the next decade, only time will tell, but the battle has begun.

On a constructive note, automakers and purveyors of the old technology are working together to make diesel vehicles ever more fuel-efficient. One of the key areas to meet this objective is by better design of the combustion chamber space. Effective combustion in a diesel engine is driven by the type of flow coming from the intake ports, the fuel injection strategy adopted, and the contours of the piston bowl. Each of these aspects is very critical and even a small improvement can lead to significant betterment in mixture formation, resulting in efficient fuel burning and reduced in-cylinder emissions.

**Figure 2:** Piston bowl geometry optimization parameters and their ranges.

Designing Piston Bowls Parametrically

The shape of the piston bowl has the latent potential to save that extra ounce of fuel. Primarily seen in diesel engines, piston bowls are recesses in the piston crown, contoured to control the air and fuel movements during the compression stroke. The grooves in the piston bowl swirl the air-fuel introduced, creating vortices that aid in effective mixing. This, in turn, results in efficient combustion which manifests as more power, better fuel economy, and reduced in-cylinder emissions such as Nox and soot.

Typically, the parametric profile of a piston bowl can be broken down into about eight adjustable features as shown in figure 2. This creates a vast parametric optimization space to pick the right design suiting our objective of minimum NOx, soot emissions, and fuel consumption. The scope of the optimization process can be further extended if aspects like the bore, stroke, squish height, compression ratio, and swirl ratio are also considered for the design.

Figure 3: Variation of a piston bowl 2D profile for a fixed compression ratio

For such design requirements, CFD can be an effective tool for picking the most optimized geometric profile. A geometric parametric modeler like Caeses in combination with a dedicated structured multiblock grid generator like GridPro and an independent CFD solver can be an effective setup for a parametric modeling-based optimization design cycle.

Figure 4: 2D parametric profile with a 3D piston bowl shape

Features in Caeses for Piston Bowl Design

Caeses comes with many features which are ideally suited for piston bowl design, some of the important ones are listed below.

The profile can be completely arbitrary in shape. The design is not limited to certain pre-defined templates. Any curve type – linear, circular segments, splines can be used. Further, the bowl profile can be varied in the circumferential direction, allowing for unique designs like ‘wavy’ bowl shapes.
Smart parameterization and dependency-based models ensure robust geometric variation with no failed variants.
The compression ratio can be automatically adjusted for each geometry variant. This is crucial for making sure that every generated variant has the same compression ratio and not wasting time on infeasible designs. It is done with an internal optimization loop, where the variables for the adjustment can be chosen freely. It is even possible to define an order of precedence so that the automated adjustment first tries to match the compression ratio with the first given variable. If that doesn’t suffice, the next variable is added, and so on.

**Figure 5:** Another example of parametric variation of piston bowl design shapes.

Other automated adjustments can be carried out as well, like adjustment of the spray angle in relation to the changing bowl shape.
The geometry can be exported in several different formats suitable for your CFD/meshing tools. Many of the formats support patch naming so that the downstream tool can correctly identify surface patches for the assignment of individual mesh settings or boundary conditions.
A design study on the piston bowl geometry can be combined with an investigation of the injection strategy, or other process parameters (such as fuel composition, EGR amount, etc.). In the software connector interface, users can parameterize and modify any value that goes into the input files or scripts for the CFD solver.

**Figure 6:** Unthinkable wavy shape created as an outcome of a parametric optimization design cycle.

GridPro’s Suitability for Piston Bowl Meshing

Flow physics evolving during the combustion process inside a piston bowl is very sensitive to the grids used to discretize the computation space. Researchers in this niche field say that hexahedral cells provide better accuracy and stability compared to tetrahedral cells. This is especially true when computations involve moving meshes or moving boundaries. Even though significant progress has been made to reduce the solver dependency on grids, the ground reality is that there is still a ‘mesh influence’ on the solution prediction accuracy in most CFD codes.

Systematic grid convergence studies for combustion chamber domains with piston bowls have shown a strong interaction of meshes with spray models and wall heat transfer models. It is observed that mesh cells are sensitive to the amount of liquid droplet mass stored in them. Finer the mesh, the larger the liquid mass percentage in that cell and the greater the evaporation. At the solver level, this issue is handled to some extent but at the cost of solution quality and accuracy.

So, here comes the catch. A finer mesh aids in improved flow accuracy predictions but is detrimental to spray evaporation modeling. Further, spray evaporation demands grid lines to align with the spray axis. The higher the injection pressure, the greater is the dependence on flow-aligned grids for meaningful prediction.

**Figure 7:** Sectional view of a 3d grid, adapting to the changing 2D contour.

Further, a large number of droplets in small thin cells around the cylinder axis during injection and combustion events leads to longer CPU times for the gas phase calculations, which in turn also leads to a loss in prediction accuracy.

Local refinement and flow alignment tools like enrichment and topology hiding in GridPro can aptly meet this requirement for coarser cells around the central axis and finer cells in the periphery. These tools help to place high-quality structured hexahedral cells at the rim of the piston bowl and smoothly coarsen them towards the central axis while still maintaining flow alignment all along this transition. It is observed that usage of such meshes can bring down the computational time by as much as 30 percent.

This mesh fineness influence can be observed even with respect to heat transfer modeling. A very fine mesh can deteriorate wall heat transfer predictions. On a mesh with a fine first spacing of the order of Y-plus less than 10, depending on the heat transfer model being used, the heat transfer gets calculated only in the laminar sub-layer and for the next layer onwards the turbulence model gets applied. This arrangement leads to inaccurate CFD prediction.

So, the right balance in cell size needs to be arrived at to make meaningful CFD calculations. Generating such tailor-made grids for every variant in an optimization cycle is a tough challenge. In a scriptable environment, GridPro can automatically generate such custom-required piston bowl meshes for every variant. The topological approach of GridPro wireframe helps to easily mesh the parametric variants of any geometry. For geometries like piston-bowl, one topology built can be used as a guide to generate grids for all the parametric variants.

**Figure 8:** Surface meshing for varying piston bowl design shapes.

Building Bridge to Build Superior Products

Shape optimization using CFD is the latest trending conversation topic among product designers. Rightly so, as it facilitates in getting a better understanding of the design space and also provides guidance to the design team in creating products with superior performance at lower risks. Further, they aid in cutting down the time involved to transfer a product from ‘design table to users table’. And lastly, optimization saves cost by avoiding expensive last-minute modifications.

They are a handy tool both in the early and advanced phases of a design cycle. In the earlier phase, they aid to explore newer ideas and possibilities and in advanced stages, their flexible and rapid responsive abilities help to make last-minute design changes. The by-product of all these positives is that it not only helps to create products of superior performance but also expands the range of product designs to choose from. They aid in the tremendous expansion of the knowledge base for making high-quality decisions.

Concluding Remark

Choosing the right optimization platform is also an important decisive step. Platforms like Caeses provide an ideal arena to conduct parametric shape optimization studies. With options to plug in any third part CFD solvers, grid-generators, or post-processing tools, Caeses turns out to be a one-stop platform for product designers. Caeses in combination with GridPro can effectively handle CFD optimization requirements in internal thermo-fluid dynamics of compressors and turbines, the external aerodynamics of cars, aircraft, the hydrodynamics of ship hulls and their propulsion systems as well as the fluid dynamics of piston bowls, mixers, valves, ducts, and pumps.

References

1. https://www.caeses.com
2. “Numerical study of the mixture stratification in an ethanol powered IC engine”, Rodrigo B Piccinini et al, Society of Automotive Engineers, Inc, 2009-36-0153.
3. “Effect of mesh structure in the KIVA-4 code with a less mesh dependent spray model for DI diesel engine simulations”, Yusuke Imamori et al, International Multidimensional Engine Modeling User’s Group Meeting at the SAE Congress, April 19, 2009, Detroit, MI.
4. “An Advanced Optimization Methodology for Understanding the Effects of Piston Bowl Design in Late Injection Low-Temperature Diesel Combustion”, C. Genzale et al, 2006.
5. “Approaching the limits of Diesel combustion efficiency”, A. Ennemoser et al, International Multidimensional Engine Modeling User’s Group Meeting at the SAE Congress, April 11, 2016, Detroit, MI.
6. “Reactive CFD in Engines with a New Unstructured Parallel Solver”, M. Zolver et al, Oil & Gas Science and Technology – Rev. IFP, Vol. 58 (2003), No. 1.
7. “Automatic Mesh Generation for Full-Cycle CFD Modeling of IC Engines: Application to the TCC Test Case”, 2014-01-1131, SAE International.