The last three stages of a lowpressure steam turbine are the focus of this study (Figure 1 and Figure 2). The objective was to optimize the three statoric rows by maximizing the totaltototal isentropic efficiency of the device for a given operating condition.
The turbine blades’ shape is defined by the position of five airfoils arranged in a spanwise direction. A Bezier distribution for both the stacking angle (for flow incidence control) and the bowing angle (for flow separation control) was used to recreate the blade shape. Another variable was used for the number of blades in the statoric row. See Figure 3 and Table 1 for details.
A parametric model is generated with these characteristics in ANSYS DesignModeler. From this point, using the ANSYS BladeEditor features, it was possible to extract the computational domain for a single passage. In fact, the first assumption made here was to consider just a single passage instead of the full wheel (Figure 4). The rotating speed compared to the mean stream velocity makes it wellsuited to a mixing plane approach. Consequently, we obtained a huge advantage in terms of the reduction of the computational costs, both as a result of the size of the CFD model and of the steady state approach with the mixing plane.
Fig 3  Blade geometry – Description of parameters
Figure 4 – Three stage, single passage – CFD model and Figure 5  Three stage, single passage – Computational grid
Another assumption made was the simplification of the actual geometry of the steam turbine: the sealings, cavities, and rotor were left out of the computational domain. This was necessary to enable a completely automatic optimization workflow, in particular for the computational grid generation of ANSYS TurboGrid (Figure 5). A grid independency study was performed to apply the best compromise between speed and accuracy. The result was a very fast and robust procedure able to achieve a highquality mesh and a welldefined boundary layer treatment for every configuration that was identified with a unique parameter set or design point.
The result of the optimization lay in the geometry for the three statoric blades. This generation depended on the simplified (“ideal”) layout of the flowpath considered here. After the optimization campaign, a final comparison between the “ideal” flow path and the actual one was performed to measure the losses created by the sealings and cavities.
Another assumption made was to consider each stage independently from the other in the optimization. In this way, the three stages, namely L0 (the last one before the diffuser), L1, and L2, were treated separately in three different optimization stages. The boundary conditions for each CFD model were obtained by combining 1D data supplied by Franco Tosi Meccanica with a preliminary analysis of the single passage, threestage turbine performed by EnginSoft.
An additional analysis of the single passage, threestage turbine was performed after each optimization stage. The baseline geometry of the statoric blade was replaced with the geometry that resulted from the current optimization stage. In this way, we could verify if the new layout of the turbine performed better than the baseline configuration. Once this was assured, the optimization continued to the next stage.
Table 1  Blade geometry – Description of parameters
Table 2  Operating constraints (with respect to the baseline configuration)
ANSYS CFX was used to set up and solve the CFD analyses. The fluid flow was considered in steady, compressible, and turbulent conditions. The advection term was resolved with a “High Resolution” scheme (bounded second order accuracy). The RANS 2 equations for Shear Stress Transport (SST) was chosen for the turbulence model. The IAPWS library was used to characterize the steam as a real fluid. The liquidvapor transition phase was considered under conditions of equilibrium. The Stage (or mixing plane) approach was considered for a multiple frame of reference (MFR). The numerical setup was optimized to achieve a good level of convergence in less than 100 iterations. In this way, each design point selected in the optimization campaign took just about 25 minutes to estimate (from the selection of the parameter set to the output of the postprocessing procedure).
The results collected by the postprocessing procedure were useful to understanding if the new design performed better compared to the baseline configuration. The objective was to maximize the totaltototal isentropic efficiency:
Fig 6  Reference for postprocessing
Several operating constraints had to be satisfied to guarantee the feasibility of a design point. For the particulars of these constraints, see Figure 6.
The choice of input parameters, output values, targets and project constraints greatly define an optimization process. Building on this point, several techniques can be selected to define which kind of optimization method is appropriate to apply to an engineering problem, especially in terms of time and cost.
Traditional engineering based on “trialanderror” was widely used in the past when automatic optimization tools were not available. Starting from a baseline configuration, the design was perturbed to get a new design point (hopefully with improved performance). The aspects of this perturbation were selected and applied by the designer and were fundamentally based on his experience. This process was repeated iteratively until the desired performance target was reached. From this description, it becomes clear that this approach cannot ever be completely automated because the decisions are made by the designer, and it is a time consuming and costly method. A schematic representation of this approach is shown in Figure 7.
Fig 7  Optimization methods – Trialanderror approach
Fig 8  Optimization methods – Direct optimization approach
Fig 9  Optimization methods – Virtual optimization approach
The evolution of this concept lead to the birth of modern optimization approaches, where algorithms replaced the designer in the selection of the new design points to be evaluated. Using efficient optimization algorithms, the parametric space can be explored broadly and intelligently in a completely automated way, in much less time compared to the traditional “trialanderror” approach.
Two different modern approaches are available:
 Direct optimization: after an initial exploration of the parameter space through a Design of Experiment (DoE), each of the design points is explicitly evaluated, with the intention of reaching a desired target. See Figure 8;
 Virtual optimization: after an initial exploration of the parameter space through a DoE, a response surface is generated to provide a continuous representation of this space. In turn, this response surface is explored using a large number of virtual design points (not explicitly simulated) in order to find good candidates. These good candidates are then explicitly evaluated, enriching the database with which the response surface can be redefined. This process is repeated iteratively until the potential inaccuracy of the response surface decreases below a certain threshold. See Figure 9.
For both the direct or virtual optimization approaches, an optimization software that is able to control the workflow that automatically manages both the exploration of different design points and the management of the fluid dynamics simulations (such as geometry generation, model preprocessing, solution and postprocessing by means of the CAE tools provided by ANSYS) is necessary. The software used for this purpose is ESTECO’s modeFRONTIER.
The modeFRONTIER’s optimization process could be split into 3 steps:

The first step includes the creation of a logical workflow to graphically formulate the engineering design problem at hand, i.e. how the simulations must be performed and in which order. The “how” implies the choice of values/measures to be used and generated (inputs and outputs), the definition of the optimization objectives and the configuration of the most appropriate algorithms to explore and optimize the design space. A representation of the optimization workflow that was defined for this study is shown in Figure 10;
 The second step consists of the evaluation of the designs, as defined by the workflow. The evaluation, or “run”, can be monitored in realtime by means of charts and graphs, and with direct access to log and process files;

The final step is the assessment and visualization of the results. The available tools allow an understanding of a problem’s important parameters on the basis of the exploration of the design space, reducing the number of significant parameters to be considered, making the optimization more efficient, rearranging the data in a comprehensible manner, and extracting a clear meaning with which to make informed decisions. Specific analysis tools help convey relevant insights into the interaction effects and to visualize optimization trends. The Response Surface Models (RSM) tool allows for the training, comparison and validation of metamodels, speeding up the entire optimization process.
Table 3  Optimization strategy
Table 4  Results of the optimization campaign
In this study, all three different approaches were used, as summarized in Table 3.
In the classical “trialanderror” approach, all the design points (almost 100) were explicitly evaluated by Franco Tosi Meccanica’s designers on their local workstations. This optimization stage took about one month to be accomplished.
For the optimization stages in which L1 and L2 were studied, EnginSoft adopted an automatic optimization procedure using modeFRONTIER™. The MultiObjective Genetic Algorithm (MOGAII) was the optimization algorithm selected for this campaign. The optimization stage for L1 required the evaluation of about 1,000 design points, while for L2 about 5,000 CFD calculations were performed. All these computations were performed on the EnginSoft cluster. A concurrent designpoints strategy was adopted to reduce the total wallclock time, so both optimization stages took about one month to complete.
The results of the optimization campaign are summarized in Table 4. The second column represents the improvement of the totaltototal isentropic efficiency evaluated for the respective turbine stage. In other words, these are the results of the three optimization stages. The last column represents the results of the additional analyses of the single passage, threestage turbine that were performed after each optimization stage. As mentioned before, in these analyses the baseline geometry of the statoric blade was replaced by the geometry resulting from the respective optimization stage.
Even though the optimization stages were independent from each other, it is clear that a good overall trend was achieved. It is important to highlight that the efficiency of the baseline design was already quite high (above 90%). From this perspective, the results achieved are very remarkable.
The last phase of the study was the evaluation of the single passage, last threestage steam turbine with its actual flowpath, i.e. including the sealings and cavities (see Figure 13 and Figure 14). A comparison between the baseline and optimized geometries of the statoric rows was performed. In real conditions, the improvement of the totaltototal isentropic efficiency achieved is about 0.5%.
Figure 11 – Comparison between baseline (left) and optimized (right)
design of the statoric blades – Blade geometry
Figure 10 – ESTECO modeFRONTIER – Optimization worklow
Figure 12  Comparison between baseline (left) and optimized (right) design of the
statoric blades – Pressure field on blades
Figure 13  Three stage, single passage – CFD model with actual sealings and cavities and
Figure 14  Three stage, single passage – Computational grid with actual sealings and cavities