To satisfy these design specifications, a virtual prototyping method has been applied. GT-Power (from Gamma Technologies), as one of the tools for the virtual engine and powertrain platform, is the analysis software used in the project for the 1D simulation of the engine and vehicle. GT-Power is used in the early stages of the engine development. However, an analysis software is not a sufficient solution for achieving the objectives included in the specifications. It does provide spot analyses though which is the key design task for the engineer in the search of the optimum. For this purpose, also modeFRONTIER has been adopted as multi-objective optimization software tool.

The GT-Power engine model is a numerical artifact that virtualizes the real behavior of the actual engine. More specifically, the 1D model simplifies the representation of such a model by reducing the real engine characteristics to lumped parameters (see Figure 2). In this article, only the geometrical entities are used as free parameters for designing the manifold. In fact, the runners dimensioning is the main goal of the optimization process.

Therefore, the actual 3D manifold geometry is “reduced” to a schematic representation (1D) as shown in Figure 3, where the parameters that define the design space are:

- Length of the runner

- Diameter of the runner’s inlet

- Diameter of the runner’s outlet

These three parameters are the only input variables to be set in the modeFRONTIER workflow. The GT-Power node is the only analysis to be run. Brake power at 5250 rpm and Brake torque at 4500 rpm are set as output values that must meet the design goals defined by the customer, such as obtaining a power of 130 HP and a torque of 188 Nm. As also reflected in the modeFRONTIER diagram in Figure 4, Power target and Torque target are the objectives of the optimization. In order to achieve both targets, a multi-objective optimization algorithm is chosen, the NSGA-II.

The results of the first optimization loop are plotted in the scatter chart in Figure 5. The chart presents the brake power on the x-axis and the brake torque on the y-axis. The square points are the simulated manifold configurations. The green circles are the individuals belonging to the Pareto frontier (the optimal designs).

It is important to understand if the optimization has achieved the design goals in order to possibly improve existing solutions. The plot in Figure 5 tells us how the optimizers strive for improving both outputs. It is equally important to see how the input parameters behaved during the optimization process. As illustrated in Figure 6, the bubble chart displays the runner’s diameter at inlet and the runner’s length. It also reflects the designs where the color (from blue to red) is related to the Torque value and where the bubble diameter is related to the Power value.

The green labeled designs belong to the Pareto frontier. The idea behind this visualization is to seek for big red bubbles, that are, by analogy, high Power and high Torque configurations. All these designs, as represented in the chart, are obviously the best solutions (the green labeled ones).

The GT-Power results are visualized in Figure 7. The plots show the functioning curves of the engines: the red curve is the initial configuration of the air intake manifold while the colored curves represent the Pareto design coming from the optimization. On the left plot, the brake power as a function of the engine speed is visualized, while the right plot points out the brake torque as function of speed. We can now understand that at 5000 rpm, the power curve of the engines with Pareto configurations is above the curve of the engine with the initial configuration. The same applies to the torque curve, where at 4000 rpm all the optimal solutions improve the original design.

The outcome of the first optimization phase is more aimed at establishing a methodology rather than at getting the optimization results themselves. This methodology might be scaled for more sophisticated manifold models. The second task is to apply the same procedure to an engine model with a more detailed parameterization of the geometry.

Instead of using only three runner parameters for the whole manifold, in this step, the runners will be split into three parts (please refer to Figure 8):

Geometry Part 1: straight duct next to the inlet described by a diameter (D) and a length (L1).

Geometry Part 2: bend duct described by a radius (r) and an angle (α).

Geometry Part 3: straight duct next to the outlet described by a length (L3) as a function of other entities given by the geometric constraints. For example, the exit out of the plenum and the admission to the cylinders are fixed, hence the runners have to vary between these two points.

Since the geometry of the manifold is now different to the first 1D model, it is necessary to develop a novel GT-Power model (see Figure 9).

A new modeFRONTIER workflow must be created, a shown in Figure 10, with the new project diagram.

As a consequence of the new model, we obtain a new Pareto set on the Power vs Torque plot (Figure 11).

As far as the values of the input variables are concerned, we can see in Figure 12 in the second optimization loop, all the parameters plotted versus the design targets.

The results of the second phase assured the designers of the reliability of this design optimization procedure.

However, during the pre-design phase, it is also important to check the quality of the 1D analysis with a 3D CFD (Computational Fluid Dynamic) model. In addition, a CFD analysis will provide relevant information for improving the fluid-dynamic response of the manifold.

Moreover, the information that GT-Power can provide on the outlet region of the flow is not as reliable as the results from a 3D CFD analysis and simulation of the pressure drop and flow uniformity. For these reasons, CFX as CFD solvers have been included in the process flow of the modeFRONTIER multi-disciplinary environment. In Figure 13, we can discern that the CFX node has been incorporated in the modeFRONTIER workflow of the second optimization phase (Figure 10).

More specifically, since the runner should also satisfy the rigid geometry boundary conditions at the outlet, the manifold geometry is modeled using the ANSYS Design Modeler. The outcome of the use of a CFD tool in the optimization loop though has not yet been completely investigated, it is still in a work-in-progress phase.

**Conclusion**

The procedure adopted for optimizing the shape of a manifold by means of modeFRONTIER demonstrates its reliability and scalability.

As demonstrated during all the phases of the project, the adoption of a properly conceived design framework (input variables, outputs, objectives...) allowed the designer to keep the focus on the most important aspects of the design like modeling the right geometry and testing more solvers (from GT-Power 1D to ANSYS CFX 3D) while satisfying the customer’s specifications and the geometry constraints.