**Introduction**

There are two main types of optimization methods available in Ansys Workbench:

- Direct Optimization
- Response Surface Optimization

This article will focus solely on direct optimization which is essentially a brute force attempt at finding the most optimal set of input values needed to produce the desired output value subject to a set of constraints. The inputs can be anything from geometry to physics. This article will use an example of trying to find the best performing airfoil using simple geometric inputs. The objective is to minimize drag while maintaining a minimum lift and lift/drag ratio. The input variables and their ranges are shown below:

*Table 1: Optimization Variables*

*Figure 1: Geometry with Chord Length, LE, TE, and Angle of Attack dimensions*

**Analysis Setup**

This analysis considers a 2D extruded airfoil with 0.2m depth created in DesignModeler and uses an airspeed of 30 MPH. After the CFD model is set up, the user creates a Direct Optimization which defines a range of values for each input parameter.

*Figure 2: Workbench Workflow*

*Figure 3: Input Variable Ranges*

Next, output constraints are added which disqualify any set of inputs that did not meet the constraints. In this case, the output constraints are a lift of at least 5N, a drag of at most 2N, and a lift/drag ratio of at least 5. For the drag constraint, the objective is set to minimize this value.

*Figure 4: Output Constraints*

After the constraints are set up, Workbench will determine an initial set of discrete input values based on the ranges provided. For each set of inputs, there is a row of data that shows the design point (DP), its input values, and its output values. The cases that are not run yet are shown with lightning bolts, and the table is filled out as the CFD runs are completed.

*Figure 5: Inputs and Outputs*

The design points shown in the table are just the initial values used to start generating an input vs output map. After these initial points are run, the optimizer will create additional points in the design space that are likely to be good candidates that meet all specified output constraints while also attempting to minimize drag. The user can choose settings that create more data points for better accuracy or decide on fewer data points in order to speed up the optimization process (the results from this example use fewer data points). Sometimes certain combinations of input variables will fail due to unphysical geometry creation or other reasons. These design points are shown with a red X. In the case of failed points, the optimizer will just disregard the data and move on to the next point.

The figure below shows the final optimized shape to minimize drag. If the optimization was allowed to use more data points, then a better-performing airfoil would be found.

*Figure 7: Optimized Shape to Minimize Drag (AoA = 5 deg)*

*Figure 8: Static Pressure Contour*

If the objective is modified to maximize the L/D ratio instead of minimizing drag, then this produces a longer, thinner airfoil at a smaller angle of attack.

*Figure 9: Optimized Shape to Maximize L/D Ratio (AoA = 2.68 deg)*

*Figure 10: Static Pressure Contour*

**Conclusion**

The Direct Optimization method is a straightforward process that allows the user to provide a simple set of inputs and constraints which Workbench then uses to determine the most optimal design. As computing resources become faster and cheaper, more of the design process will be spent using automated optimization methods so that the engineer can spend more time on the higher-level decisions and less time generating geometries, meshes, and pre/post-processing.

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