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The present paper proposes a methodology to design and manufacture optimized turbomachinery components by leveraging the potential of Topology Optimization (TO) and Additive Manufacturing (AM). The method envisages the use of TO to define the best configuration of the rotoric components in terms of both static and dynamic behavior with a resultant reduction of overall weight. Eventually, the topology-optimized component is manufactured by using appropriate materials that can guarantee valid mechanical performances. The proposed strategy has been applied to a 2D impeller used for centrifugal compressors to prove the effectiveness of a TO+AM-based approach. Although this approach has never been extensively used before to centrifugal compressors and expanders, its application on rotor and stator components might unlock several benefits: tuning the natural frequencies, a reduction in the stress level, and a lighter weight of the rotating part. These objectives can be reached alone or in combination, performing a single analysis or a multiple analyses optimization. Finally, the introduction of AM technologies as standard manufacturing resources could bring sensible benefits with respect to the time to production and availability of components. Such aspects are essential in the Oil and Gas context, when dealing with new projects but also for service operations.

The increasing requirement for energy demands for highly efficient turbomachinery systems [

CNC milling is the current golden standard for the manufacturing of single-piece impellers as it is able of reliably fabricating complex shapes (see Figure

Some examples of impeller milling processes.

When dealing with impellers characterized by narrow passage and simple flow passage, an elective process is the Electrical Discharge Machining (EDM). This method (see Figure

Impeller EDM operations.

It is important to highlight that the evolution of high-efficiency rotors has brought towards lighter structures that need to sustain higher speeds. Indeed, traditional subtractive technologies are less suited for the fabrication of slender structures, as the removal of higher volumes of materials is required. Additionally, modern design software allows shape optimizations in a relative short time, leading to complex geometries unconstrained from conventional mathematical surfaces. In this context, Topology Optimization (TO) software systems are among the most used design tools. Thanks to advanced optimization algorithms, they are able to improve the material distribution within a given design space for a given set of loads and boundary conditions such that the resulting layout meets a prescribed set of performance [

Consequently, the adoption of AM for the fabrication of TO-produced designed usually represents a convenient choice because of the complexity of the shapes, which are produced with minimum attention at fabrication constraints. AM offers also significant advantages due to its short lead times and great geometrical freedom. This advantage makes AM the natural prosecution of TO processes [

Dealing with the fabrication of impellers, the interest is directed to metal-based processes. In the last 5 years, metal AM process has seen great improvement in terms of mechanical performances of the parts produced and reliability and predictability of the process. As a result, metal AM processes are now an established alternative to traditional subtractive ones even for the fabrication of mechanical parts that need to sustain significant structural loads. According to [

In [

Based on the above-mentioned considerations, the present paper proposes a unified approach for designing and manufacturing optimized turbomachinery components by leveraging the potential of Topology Optimization (TO) and Additive Manufacturing (AM). The method envisages the use of TO for defining the best configuration of the rotoric component in terms of both static and dynamic behavior with a resultant reduction of overall weight. Eventually, the topology-optimized component has been fully manufactured (both in Aluminum and in high resistance alloy like IN718) by using appropriate materials that can guarantee valid mechanical performances.

Specifically, the 3D printer technologies considered in this work are based on sintering through laser beam or electron beam; both processes are expensive and characterized by high-energy consumption. Moreover, final parts have surfaces with high porosity and surface roughness when compared with the ones obtained using traditional milling. Accordingly, postprocessing operations are usually required to obtain the desired quality. On the other hand, the possibility of manufacturing optimized parts with better performances in terms of static and dynamic behavior and lower weight encourages the effort to push forward AM in the turbocharger sector.

Even if the methodology is fully general, to prove the effectiveness of the proposed TO+AM approach, a specific high pressure impeller of a centrifugal compressor has been chosen as test case in this paper due to the critical characteristics of this application in terms of geometry and working conditions.

Finally, it is noteworthy that the approach presented in this paper, if extensively applied to rotating turbomachinery components, might unlock several benefits: tuning the natural frequencies, a reduction in the stress level, and a lighter weight of the rotating part, thus enabling higher speeds and improvement of thermodynamic performances. The design of structurally efficient shapes can lead, in turn, to a weight reduction of the parts, with a consequent abatement of costs.

As mentioned above, the present work aims to describe a method for designing optimized rotoric components used for Oil & Gas sector (e.g. turbine disks or impellers) and for additive manufacturing of them. Some constraints, detailed in the text to follow, are taken into account with the aim of manufacturing efficient impellers:

the material used for the component that should guarantee the following properties: high ductility at different operating temperature (that can go from cryogenic up to 400°C);

corrosion resistance induced by the presence of water and CO_{2} and in presence of H_{2}S;

pitting resistance induced by the presence of chlorides;

high strength to sustain the working condition (pressure and speed);

market availability of the material, in order to keep low supply times and cost.

Therefore, the proposed design method is based on the following steps (Figure

Step

Step

Step

Step

Step

Framework of the proposed design method.

The overall process and the tools used to perform each step will be described with reference to a specific test case (i.e., a centrifugal compressor impeller, detailed in the text to follow) in order to present the method with a practical approach. As a result, test-case specific information (design specifications, constraints, and geometry) is provided in each step to discuss the application of the procedure. Whereas specific aspects of the chosen test case are provided throughout the entire manuscript, the intent is to provide the reader with a general comprehension of the method.

Compressors are the parts of an engine responsible for providing enough air with enough pressure to the combustion chamber. In most cases, gas turbine engines have two compressors: low-pressure and high-pressure, which operate at different working temperatures. The low-pressure compressor usually works at relatively low temperatures, around 350°C, whereas the high-pressure compressor works at temperatures in the range of 500°C to 600°C. Accordingly, the selected test case is a 2D impeller (i.e., an impeller characterized by two-dimensional blades in the radial part) used in centrifugal compressors [

Specification of analyzed stage.

Flow Coefficient | 0.0444 |

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Mach | 0.73 |

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Diameter [mm] | 390 |

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GE impeller used as a starting point for carrying out the novel design.

Moreover, the impeller is considered as composed by a material with linear elastic isotropic properties as listed in Table

Material Properties.

Young’s Modulus (E) | 2.2^{5} MPa |

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Poisson’s Ratio ( | 0.3 |

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Density ( | 7.85^{3} kg/m3 |

Prior to optimizing the design of the selected case study, it is necessary to perform its complete characterization in terms of both static and modal behavior. This characterization, carried out by means of a Finite Element Analysis (FEA), provides the baseline for assessing the performance of topologically optimized design. In particular, the FEA allows to estimate both the maximum displacement and the maximum stress of the impeller (see Table

Maximum stress in the whole impeller and maximum radial displacement in the interference region between impeller and shaft.

Maximum stress [MPa] | 561 |

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Maximum displacement [mm] | 0.14 |

The boundary conditions imposed during the FEA are as follows:

Two nodes at impeller front hub constrained in the tangential direction.

Two nodes at impeller back hub constrained in the axial direction.

The only external load applied to the rotating component is a static loading condition due to a centrifugal force field (see Equation (

The distribution of von Mises stresses on the benchmark geometry is depicted in Figure

Stress distribution obtained by FEM on the benchmark geometry.

The impeller was characterized also by means of a modal analysis since the main objective for the subsequent TO is to move away from the operating range particular vibrating modes (i.e., away from the frequency range near the working frequency

Impeller natural modes.

Mode | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Frequency (Hz) | 33 | 33 | 38 | 38 | 44 | 48 | 48 | 49 | 49 | 50 | 50 | 56 | 56 | 58 | 58 | 63 |

00 | 01 | 32 | 33 | 92 | 54 | 55 | 66 | 67 | 27 | 28 | 63 | 64 | 82 | 83 | 61 |

When a generic TO has to be carried out, it is necessary to define the design space, i.e., an area enclosing the set of elements that can be changed during the optimization. Oppositely, the nondesign space defines model regions that remain unchanged during the optimization routine. Referring to the selected test case, the blade region must be preserved; accordingly, it belongs to the nondesign space. The analysis design space to be considered includes both hub and shroud regions. A graphical explanation of design and nondesign space is given in Figure

TO domain: design and nondesign space.

In the formulation of optimization problems, some quantities can be used as objective function to be minimized (usually global quantities) and some others as constraints (usually local quantities): compliance, natural frequencies, volume (or volume fraction), mass (or mass fraction), displacements, stresses, and strains.

The minimization of objective functions drives the seek for an optimized shape. Two main strategies have been tested in this work: minimizing the volume and minimizing the compliance. The minimization of the volume (see (

On the contrary, compliance minimization is very interesting and promising also according to literature studies [

The compliance is the strain energy of the structure and it can be considered a reciprocal measure for the stiffness of the structure. It is defined for the whole structure, since the objective functions must be referred to a global parameter. The objective of the minimum compliance problem is to find the material density distribution that minimizes the structure deformation under the prescribed support (boundary conditions) and loading conditions.

The optimization constraints used in this work are on the displacements in the area of interference between the shaft and impeller (in order to avoid detachments), on the maximum value of the stress and on the volume fraction (see (

The various constraints can be defined as follows:

In the proposed framework, the TO problem is carried out by using the Solid Isotropic Material with Penalization (SIMP) method [

The constraints on stress, displacements, and volume, introduced in the previous step, are set as follows:

u max < 0.100 mm;

The centrifugal load acting on shroud, blade, and hub can be described as follows:

Finally, a further set of constraints is imposed with the aim of performing modal optimization:

mode 10, 11 frequency < 5475 Hz;

mode 12, 13 frequency > 5785 Hz.

The main objective of the modal constraints is to move away from the operating range particular vibrating modes (see Table

The best performance for the static and modal topological optimization is reported in Figure

2D impeller optimization results.

Baseline | Optimization | Reduction | |
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Maximum stress [MPa] | 561 | 408 | 27% |

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Maximum displacement [mm] | 0.14 | 0.10 | 28% |

Optimization result for the 2D impeller.

At this step of the research activity, the dynamical loads have been considered into the optimization procedure in terms of frequency constraints to keep the modal frequencies of the optimized system away from the “most probable” frequency operating range of the machines. At the same time, since the operating conditions of the machine at such frequency may be quite variable and different from the nominal one during the machine life, the authors did not apply a specific dynamical load in terms of harmonic pressure field on the blades of the compressors. This harmonic pressure field would be, indeed, related to a specific machine working condition, and not fully representative of the pressure loads acting on the machine during its entire life. However, during the next step of the research activities, numerical and experimental fluid dynamical analyses will be performed “a posteriori” to verify the performances of the optimized components under specific operating conditions.

The results in terms of modes are summarized in Table

Baseline and optimized Impellers natural modes.

Mode | Baseline Freq. (Hz) | Optimized Freq. (Hz) |
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11 | 5028 | 5462 |

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12 | 5663 | 5795 |

Furthermore, it has to be highlighted that the algorithm has removed mass at the zone at higher diameter, which is the area that vibrates more, reducing the stiffening of the structure. At the same time, to keep the stress level below 500 MPa, a series of reinforcement along the blade tip are created, together with a concentration of mass on the eye region, above the blade leading edge. These features are able to reduce the stiffness of the impeller by keeping at an acceptable level both blade deformations and stresses.

It is important to note that, in this phase of the research activity, the target is to perform the structural optimization of the component. In particular, the dependence of the material characteristics on the temperature (thermal expansion, Young modulus, etc.) has been considered, but the working temperature has been kept constant. In other words, a complete thermostructural optimization (involving the optimization of temperature and thermal flux, and computationally much heavier) has not been performed yet.

However, during the next step of the research activities, numerical and experimental thermal analyses will be performed “a posteriori” to verify the performances of the optimized components under specific operating conditions. Furthermore, a complete thermostructural optimization of analogous components and of components working at higher temperatures will be performed. For high temperature components, high resistance titanium alloys will be considered as well.

As already mentioned, the optimized geometry of the impeller is not obtainable using traditional subtractive technologies and therefore the only viable way to manufacture it is to adopt AM. Since the desired model is not a mere mock-up of the impeller but rather a fully operating prototype, metal AM is the elective technology to produce such a part. Therefore, a preliminary analysis of most promising materials for turbomachinery applications was conducted. One of the most interesting materials investigated, is the IN718 [

In detail, using both direct metal laser sintering (DMLS) and traditional forging a number of specimens are produced. Then, such specimens are tested to compare their performance. For a design standpoint, a complete characterization of the materials has been performed exploring fatigue and tensile properties of the material, directly compared with the corresponding wrought alloy. A good matching of the characteristics is obtained after welding parameters set up phase finding that the DMLS specimen has a better ductile behavior, that is found in both higher elongation and lower UTS at lower temperature. Variability in the DMLS process is comparable to the forging one since the data statistically processed shows approximatively the same standard deviation for the two processes.

Furthermore, a metallographic examination has been carried out; Figure

Metallographic examination results: (a) 0.2% tensile yield strength comparison; (b) UTS comparison; (c) wrought IN718 micrographic examination; (d) DMLS IN718 micrographic examination.

Moreover, corrosion resistance behavior is in line with wrought material. In conclusion, it is possible to prove that the 3D printed IN718 may be considered a very good alternative to forgings, at least for components sizes that are within printable dimensions, as also demonstrated by scientific literature [

After the material characterization has been carried out, showing the good mechanical properties of the selected alloy, it is possible to manufacture the optimized component. As already mentioned, the selected technology is the DMLS additive manufacturing. High-precision DMLS parts possess exceptional surface characteristics along with mechanical properties equivalent to those found in traditional wrought materials after that proper heat treatment is carried out [

In detail, the machine adopted to create the prototypes is the EOS M400, with a volume capability of 400x400x400mm. Since the designed component is characterized by unusual geometries, also due to the very low flow coefficient (i.e., below 0.0100) which encompasses very narrow blade passages, prior to manufacture of the model using IN718 powder, a dummy model has been realized. The selected material to create such a model is aluminum. The steps followed to obtain the prototype are as follows:

definition of the model position and orientation within the machine building volume. Such step should be carefully carried out in order to reduce the incidence of thermal deformations and residual stresses to the manufactured part. Moreover, even surface quality can be affected by the orientation of the part: this aspect should be taken into account to reduce the need for postprocessing operations.

deposition and melting of metal powder as per DMLS process, tuned to increase the geometrical quality of the dummy part;

heat treatment of the part produced to reduce deformation induced by the AM process;

removal of the internal support, needed to sustain overhang structures at angle above 45°;

final machining to achieve the desired external geometry;

finishing process to reduce the final roughness in the flow path region.

The process parameters have been tuned according to the proprietary know-how of BHGE and studies available in literature (e.g., [

Optimized compressor impeller produced in Aluminum.

To verify the effectiveness of the additive process to create the prototype, a number of dimensional measurements were carried out to verify the compliance of the model with geometric dimensions, tolerances, and roughness. Measured dimensions are in Figure

Impeller dimensions outside requested tolerances.

Parameter | Description | Difference vs nominal |
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B3 | Inner Diameter | -0.01% |

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C1 | Foot length | 2.27% |

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C2 | Total length | 1.38% |

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BB | Seal diameter | -0.03% |

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B11 | average exit width | -3.86% |

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D21 | Average Disk thickness at exit | 11.11% |

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D24 | Average Shroud thickness at exit | 52.78% |

Dimension definition for geometrical control.

The final geometries were within the requested dimensional and geometrical tolerances, with a final roughness achieved through abrasion flow machining. The main differences are measured on the hub and shroud thickness at the exit region; however, it is possible to machine the external part to achieve the required dimensions.

Given for granted the good results obtained for the dummy Al model, the final step consisted in manufacturing the IN718 final prototype (see Figure

Final prototype of the impeller.

Along this paper an introduction to innovative manufacturing process and related design approaches has been presented, highlighting the strength and the weakness of both and showing how the printing techniques shall be thought not just as an alternative to conventional processes but as a new technology enabling generating geometries that could not be imagined before. The results reported show how topological optimization gives promising results in terms of mass reduction and stress optimization dynamic response of the structure and that many design space constraints can be removed if coupled with additive manufacturing techniques. Significant improvements in terms of mechanical performance have been achieved: the stresses values and the radial displacements of the interference zone have been reduced if compared to traditional design, decreasing the impeller weight as well. The resulting structure is lighter and satisfies all design constraints. This aspect has allowed raising rotational velocity and then the machine efficiency.

The best configuration of constraints and objective functions to obtain new components structures was defined. The best strategy to obtain promising results is minimizing the total compliance, with constraints on local stress, displacement, and volume fractions. The “ready to print geometry” can be produced by a rendering process, after each optimization to create a smooth 3D model for the manufacturing.

Concerning the future developments of the research activity, numerical and experimental fluid dynamical analyses (in aluminum and IN718) will be performed to verify the mechanical characteristics of the optimized components under specific operating conditions [

Overall, the main goal of the new research steps will be the optimization of the whole production process (structural optimization; additive manufacturing; post–AM treatments). To this end, new and more extreme structural optimization techniques (as, for example, lattice topology optimization) will be taken into account.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

The authors would like to thank “BHGE, a GE Company” for the precious support during all the phases of the research activity and for providing the required technical documentation.