Computer Aided Drafting, Design and Manufacturing Volume 25, Number 3, September 2015, Page 1

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1 Computer Aided Drafting, Design and Manufacturing Volume 25, Number 3, September 2015, Page 1 CADDM A Turbine Blade Parametric Modeling Method Considering 1-D Heat Transfer Analysis LI Ji-xing 1, XI Ping 1, GUO Yan-fei 2, ZHANG Jian-qi 3 1. School of Mechanical Engineering and Automation, Beihang University, Beijing , China; 2. School of Software Engineering, Beihang University, Beijing , China; 3. School of Mechanical Engineering, Northwestern Polytechnical University, Xi an , China. Abstract: Traditional feature-based turbine blade models can match the needs of geometric modeling but could hardly meet the requirement of data extraction in 1-D heat transfer analysis. In this paper, the requirements of data extraction in 1-D heat transfer analysis are taken into consideration as well as geometric representation in parametric design process. An improved turbine blade parametric modeling method is proposed. Based on the modeling method proposed, a system structure of blade modeling process considering 1-D heat transfer analysis is devised. Eventually, a turbine blade parametric modeling system is constructed to test and verify the feasibility of the proposed modeling method and system structure. Experiments show that the blade parametric modeling method proposed can make geometric models better adapt to the specific requirements of 1-D heat transfer analysis and has certain reference value to the creation of high quality digital models. Key words: turbine blade; parametric modeling; 1-D heat transfer analysis; data extraction 1 Introduction Digital product modeling technology is the foundation of digital design and manufacture; it includes the digital representation, description, simulation, transfer and conversion of digital models [1]. Feature-based parametric modeling technology (referred to as FPM) is a predominant way to fetch digital product models [2]. According to product s geometric structure, FPM accomplishes modeling through feature analysis and parametric design process and modifies the model through dimension-driven mechanism [3]. The Original intention of the combination of digital geometric modeling technology and product design is to realize NC machining of complex surfaces [4]. However, in addition to meet the need of shape description, digital model also need to provide effective geometric representation as input for the simulation analysis process now days. The applicability of digital model in the process of simulation analysis directly affects the feasibility and efficiency of the digital design process. At present, integration technology of CAD and CAE has become a hot issue in the field of digital design. Take the aeroengine blade design as an example to discuss the role of digital model in the whole design process. As showed in Fig. 1, the general process of turbine blade design is structure design, simulation and then blade structure modification according to the simulation result [5]. This design cycle will not stop unless the blade structure and related simulation result meet the design requirement. The cooling structure design is an important step in turbine blade design. The general design process is preliminary design, structure design, simulation, structure modification. The design is an iterative process based on digital models, so the quality and adaptability in different design steps of the digital model have important significance for the efficiency and quality of 1-D heat transfer analysis (pipe-network calculation) and 3-D conjugate heat transfer simulations. In the field of blade cooling structure parametric design, most studies focus on the realization and representation of blade geometry, only few studies take subsequent analysis into account in parametric design. The most active research to bridge the gap between computer aided design and finite element analysis (FEA) nowadays is the isogeometric analysis (IGA) Corresponding author: XI Ping, Female, Ph.D., Professor, xiping@buaa.edu.cn.

2 2 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.25, No.3, Sep introduced by Hughes et al. [6]. Its core idea is to use the same basis functions for the representation of geometry in CAD and the approximation of solution fields in FEA. This strategy bypasses the mesh generation process required for standard FEA and supports a tightly connected interaction between CAD and FEA tools [7-9], which could potentially reduce the time required for the analysis of complex engineering designs by up to 80% [6,10]. IGA has been used in turbine blade design and demonstrate the capabilities of isogeometric analysis in a real-world industrial environment with challenging numerical simulation problems. Opstal et al. [11] introduced an isogeometric method for CFD and FSI-simulation of flow around turbine blades. Großmann et al. [12] studied the deformation of blades of aircraft engines under the influence of centrifugal forces, air pressure, and inhomogeneous temperature distribution. In addition to IGA, some other methods are also studied in the field of blade design to narrow the gap between CAD and CAE. Chen [13-14] proposed an analysis-oriented parametric modeling method to make the digital model meet the requirement of finite element pre-processing and take the turbine blade as an example to validate the modeling method. Tang et al. [15] presented a finite element parametric modeling technique of aircraft wing structures and this technology has certain reference on blade modeling. Wang et al. [16] designed a Unit Design Method to integrate the 1-D heat transfer calculation and the parametric design of cooling structures, but the models created by UDM are brief and could not be used in any other design steps except the pipe-network calculations. In the current study, there is no mature modeling method which can realize the integration of parametric design and analysis in blade design, and the existing parametric model is difficult to run through the whole design process. Moreover, these studies put more emphasis on grid generation in 3-D simulations rather than data extraction in 1-D heat transfer analysis. In this paper, we analyzed 1-D heat transfer analysis s demand for digital model and propose a parametric design method considering 1-D heat transfer analysis (referred to as BHTAM) to achieve seamless integration between blades modeling and 1-D heat transfer analysis. 2 Modeling Requirements of 1-D Heat Transfer Analysis 2.1 Brief Introduction of 1-D Heat Transfer Analysis The 1-D heat transfer analysis based on empirical formula is a traditional thermal analysis method with fast calculation speed and high reliability, and commonly used to guide the scheme design of turbine blade [17-18]. It converts 3-D cooling structures in turbine blade to 1-D structures according to some approximate conditions and assumptions and then establishes a thermal calculation model (also called pipe-network calculation model) to perform thermal analysis [19]. In 1-D heat transfer analysis, the most time confusing step is the process of converting 3-D models to pipe-network calculation models, which need divide the blade models into several 3D entity units and extract lots of geometric data on each 3D entity unit. Just as showed in Fig. 2, the 3D entity units can be classified into several types based on their geometry structures. Every 3D entity unit is corresponding to a compute node in pipe-network calculation model and the geometric data is extracted for heat transfer analysis and input into the calculation model. Relatively, extracting parameters for heat transfer analysis automatically in 3D entity units is much more complex than dividing blade models into entity units because of the amount of data and the extraction method. Take the pipe elbow unit as an example, parts of parameters needed to be extracted are listed in Table 1 and some of the parameters are showed in Fig. 3. Scheme Design Detailed Design Fig. 1. Original Design Parameters Preliminary Design A Variety Of Primary Cooling Structures Parametric Design Of Cooling Structures Pipe-network Calculation Of Cooling Channel Alternative Cooling Structures Parametric Design Of Cooling Structures Conjugate Heat Transfer Simulation The Adopted Cooling Structures Modify Modify Turbine blade cooling design procedure.

3 LI Ji-xing et al., A Turbine Blade Parametric Modeling Method Considering 1-D Heat Transfer Analysis 3 connected relation of blade solid unit serial number of blade solid unit connected network of blade unit Fig. 2. Pipe-network model and its entity units of turbine blade. Table 1. Parameters for Heat Transfer Analysis in Pipe Elbow Unit Parameter Description Extraction Method r Round radius Radius of two upper round among inner surfaces in pipe b 0 Width at pipe inlet Length of curve intersected by pipe middle surface and inlet surface b k Width at pipe middle Height of pipe inner wall minus height of rib R 0 Turning radius of pipe (r 1 +b k )/2 F 0 Cross-sectional area at inlet Cross-sectional area at pipe inlet U Wetted perimeter length at inlet Wetted perimeter length at pipe inlet Al k Width of rib Width of rib between suction surface and pressure surface Al Length of center line Length of the center line of pipe Ac Heat transfer area within unit Area of all inner surface except the surface in ribs of two side Ag Heat transfer area outside unit Area of suction surface and pressure surface among outer surfaces Aw Heat transfer area (Ac+Ag)/2 δ Wall thickness Average thickness of the pipe wall λ w Thermal conductivity of materials Global parameter pointed by designers r 1 Inner radius of rotation Height of bottom plane in unit r 2 Outer radius of rotation Height of the top surface in all inner surfaces Fig. 3. r Some parameters to be extracted. Traditionally, structure designers divide the blade model and extract the geometric data manually to establish the pipe-network calculation models. Because of the large number of parameters and entity units, it costs lots of time and energy and designers must spend lots of time to understand the meaning of parameters for thermal analysis. To improve the efficiency of 1-D heat transfer analysis, we studied the automated construction of pipe-network calculation model by using the method of geometric element recognition and these studies indicate that the feasibility, efficiency and accuracy of data extraction are not possible to guarantee without matching parameterized blade models [20].

4 4 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.25, No.3, Sep Requirement Analysis of Modeling Considering 1-D Heat Transfer Analysis By the parameter descriptions listed in Table 1, we can know that parameters for heat transfer analysis (referred to as PHTA) are different from parameters for structure modeling (referred to as PSM). Most of the PHTA are difficult to be gotten from PSM directly or indirectly while few can be calculated through modeling parameters such as the parameter r. The core of data extraction algorithm is recognizing geometric elements referring to PHTA automatically. Then we use parameter U in elbow pipe unit as an example to describe the thought of the data extraction algorithm. Step 1. Get all faces and edges from the entity unit model; Step 2. Calculate the geometry property and topology relationship of these faces and edges such as the bounding box, face type, edge type and so on; Step 3. Define F showed in Fig. 4 according to its geometry property, F can be regard as a plane with the minimum Z value. Step 4. Select plane F from all faces in the entity unit according to its definition; Step 5. Get all the edges from the face F, and divide these edges into 3 groups while edges in each group can form a closed loop; Step 6. Get the loop we need from these 3 loops, and the Loop_2 is corresponding to the parameter U. Step 7. Calculate all the lengths of edges in Loop_2, and the sum of these lengths is the value of U. modeling method try to make the geometric elements related to PHTA exist and easy to identify in addition to the traditional geometry shapes. Based on this premise, disadvantages of the current blade modeling method are illustrated as follows: (1) Functional structure decomposition method adapted to entity unit classification is not adopted while we divided turbine blades into different structures at the stage of modeling framework design. (2) Modeling methods adapted to subsequent heat transfer analysis are not adopted while modeling. As shown in Fig. 5, taking same sections as input, different modeling methods can generate identical solid models and distinct wireframe models. Model generated by method B will surly has fewer faces and edges thus to reduce the difficulty of geometric elements recognition. (a) Cross sections (b) Solid model (c) Wireframe model with curve mesh method (d) Wireframe model with lofting method Fig. 5. Effects of two different modeling methods in NX. Fig. 4. Extraction method of parameter U. From the example above, we can conclude that the recognition difficulty of geometric elements in the model basically determines the difficulty of data extraction. So1-D heat transfer analysis requires the (3) Modeling specification affiliated with heat transfer analysis process is not adopted. For example, only one kind of modeling method should be adopted in the same type of structure modeling process to avoid confusion in the process of geometric elements recognition; the number of the same kind of feature should be standardization and continuity so we can visit these features according to their name and number.

5 LI Ji-xing et al., A Turbine Blade Parametric Modeling Method Considering 1-D Heat Transfer Analysis 5 (4) Intermediate modeling data is not conserved. For example, the intersect points between film hole axis and the outer surface of blade which no longer exists after the generation of holes. (5) Lacking of ability to patch topological fragments to ensure topology correctness. (6) Auxiliary features are not generated or marked. Only relying on geometric elements in blade structures always leads to the horns of a dilemma. As shown in Fig. 6(a), the entity unit divided directly could not be accepted by the follow-up procedure. Therefore, subsidiary sheets need to be constructed in geometric model according to needs of blade separation. (a) Entity unit divided by direct separation (b) Entity unit divided by auxiliary sheet All the disadvantages above indicate that although blade models generated by traditional blade parametric design method can perfectly represent geometric shapes, it can hardly satisfy the demands of subsequent heat transfer analysis, which sets obstacles for data extraction in pipe-network calculation. Therefore, a new parametric modeling technology which can combine geometric modeling and heat transfer analysis data extraction procedures tightly and make the whole design passage easy and smooth is necessary to be studied. 3 Turbine Blade Modeling Method Considering 1-D Heat Transfer Analysis In order to adapt the blade model to analysis of heat transfer better, taking modeling requirements of subsequent heat transfer analysis into consideration simultaneously with parametric modeling is the only way. Based on traditional blade modeling method, blade modeling technology considering 1-D heat transfer analysis meets more needs of data extraction by analyzing the disadvantages and supplementing or adjusting certain stages of the traditional method. The flow chart of BHTAM is showed in Fig. 7. Flow chart of traditional blade modeling method is marked by the solid line box and the distinctions between these two modeling methods are shown outside the box in the figure. Promotions towards traditional method are reflected mainly in the following six aspects: Fig. 6. Effect of direct/auxiliary entity separation. Fig. 7. Flow chart of blade modeling BHTAM. (1) 1-D heat transfer analysis adapted functional structure decomposition method: Turbine blades are

6 6 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.25, No.3, Sep complex products with multiple functional structures and generally decomposed into a plurality of functional structures to create respectively so that the difficulty of modeling and maintenance could be reduced. Adopting functional structure decomposition suited to entity unit classification is beneficial to turbine blades division and data extraction automatically. (2) 1-D heat transfer analysis adapted modeling functions: Modeling functions of CAD software which are adapted to data extraction process should be chosen while modeling in order to get a rational wireframe model and reduce the difficulty of geometric elements recognition. In addition to the example showed in Fig. 5 about rational wireframe, different modeling functions will also lead to different geometry property. For example, the ribs in blade could be create by sweep function using the section and guideline in Fig. 8 while could also be create using the equidistant surface method proposed by Yang et al. [21]. Relatively, the faces in ribs created by the latter method are easier to identify because they can be classified into plane and offset surface while faces created by sweep are all B-Surface (NURBS surface). Fig. 8. Section and guideline for ribs. (3) Modeling specification affiliated with 1-D heat transfer analysis: Modeling specification in modeling process according to the demands of 1-D heat transfer is of significance to geometric elements recognition. The modeling specification is much stricter than in traditional modeling method s because traditional modeling method merely concern about the correctness of geometric shapes and need not put too much emphasis on parameters management and geometric elements recognition. Under the circumstance of modeling specification affiliated with 1-D heat transfer analysis, the choices of modeling method becomes fewer, which can be recognized as a sacrifice for subsequent analysis. (4) Mid-data conservation: According to need for extracting heat transfer data, intermediate modeling data should be conserved in some certain way during modeling so as to meet the demands of data extraction later on. (5) Topological fragments reparation: After geometric modeling, it is necessary to check for any topological fragments and repair these fragments as much as possible by adjusting model functions or modeling sequence of features. (6) Auxiliary features generation and marking: In or after geometric modeling, auxiliary features should be constructed according to certain parameters extraction strategy to provide valid assistance for geometric elements recognition. 4 Turbine Blade Modeling System Considering 1-D Heat Transfer Analysis 4.1 Logical Architecture Design of Turbine Blade Modeling System On the basis of traditional blade modeling method, the frame system structure of BHTAM is proposed as shown in Fig. 9. In this system structure, filters, drivers and the parameter solver is the core parts while these sets are external support facilities. The knowledge about 1-D heat transfer analysis is encapsulated in these filters, solvers, drivers and sets. The parameter solver is designed to convert the original design data such as aerodynamic parameters or heat transfer parameters into geometric modeling data so that the geometric modeling module can be connected with the upstream module. The decomposition knowledge set is used in the logical design of these system and don t participate in system implementation. Data filter is responsible for analyzing input data and ensuring the correctness and usability of data passed to modeling process while the method filter is responsible for filtering out immature geometric modeling methods so as to reduce difficulty of geometric elements recognition. The task of geometric modeling driver is to mark features corresponding to information of rule sets as well as conserve mid-data of modeling process. What s more, the driver runs according to the modeling specification in model specification set. Post processing driver is responsible for auxiliary features generation and fragments reparation according to the connected method and rule sets. 4.2 Implementation Results of the Turbine Blade Modeling System According to the logical architecture above, a turbine blade modeling system considering 1-D heat transfer analysis is developed based on UG so as to test and verify the feasibility of the proposed modeling technology and system structure. Fig. 10 shows the functional structure of turbine blade which is adapted to 1-D heat transfer analysis; Fig. 11(a) displays the final wireframe model of

7 LI Ji-xing et al., A Turbine Blade Parametric Modeling Method Considering 1-D Heat Transfer Analysis 7 turbine blade via the modeling system; Fig. 11(b) provide an example of auxiliary feature for splitting the trailing edge slots; Fig. 11(c) demonstrates an topology fragment error; Fig. 12 shows the segmenta- tion results and data extraction results of the turbine blade as well as the pipe-network model established by program based on the blade model generated by the modeling system. Fig. 9. Structure for BHTAM. Fig. 10. Functional structure of the blade modeling system.

8 8 Computer Aided Drafting, Design and Manufacturing (CADDM), Vol.25, No.3, Sep Topology error Topology Reparation (a) Wireframe model (b) Auxiliary features generation and marking (c) Topological fragments reparation Fig. 11. Illustrations of turbine blade modeling system considering 1-D heat transfer analysis. Fig Conclusions Data extraction result of 1-D heat transfer analysis model. Based on traditional feature-based turbine blade modeling method, we proposed a new turbine blade modeling method considering 1-D heat transfer analysis and its corresponding system structure. And a turbine blade modeling system was developed according to the method and system structure proposed in the article was testified. The experiment shows the turbine blade modeling method considering 1-D heat transfer analysis is capable of generating geometric models well adapted to the demands of data extraction thermal analysis, which has certain reference value for the creation of high-quality digital models. References [1] Yan C L, Yang F F. The New Technology of Digital Design of Machinery [M]. Beijing: China Machine Press, 2007: [2] Ye X Z, Peng W, Tang R X. Review of development history of the international CAD industry and some lessons learned [J]. Journal of Computer-Aided Design & Computer Graphics, 2003, 15(10): [3] Song Y W, Xi P. Parametric design of turbine blade Using feature-based modeling technology [J]. Journal of Beijing University of Aeronautics and Astronautics, 2004, 30(4): [4] Zhang T, Cui Z Q, Hou J H, et al. Modeling technologies and their features in CAD evolution [J]. Mechanical Engineering & Automation, 2011, (6): [5] Chi Z R. Heat Transferring Design for Air-cooled Turbine Blades [D]. Harbin: School of Energy Science and Engineering, 2011 (in Chinese). [6] Hughes T J R, Cottrell J A, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement [J]. Computer Methods in Applied Mechanics & Engineering, 2005, 194(s39-41): [7] Kagan P, Fischer A. Integrated mechanically based CAE system using B-Spline finite elements [J]. Computer-Aided Design, 2000, 32(s8-9): [8] Cohen E, Martin T, Kirby R M, et al. Analysis-aware modeling: understanding quality considerations in modeling for isogeometric analysis [J]. Computer Methods in Applied Mechanics & Engineering, 2009, 199(5-8): [9] Schmidt R, Kiendl J, Bletzinger K U, et al. Realization of an integrated structural design process: Analysis-suitable geometric modelling and isogeometric analysis [J]. Computing & Visualization in Science, 2010, 13(7): [10] Cottrell J A, Hughes T J R, Bazilevs Y. Isogeometric analysis: toward integration of CAD and FEA [J]. Wiley & Sons, 2009, (5): [11] Opstal T V, Fonn E, Holdahl R, et al. Isogeometric methods for CFD and FSI-simulation of flow around turbine blades [J]. Energy Procedia, 2015, 80(1): [12] Großmann D, Jüttler B, Schlusnus H. Isogeometric simulation of turbine blades for aircraft engines [J]. Computer Aided Geometric Design, 2012, 29(7): [13] Chen R Z, Xi P. Analysis-oriented parametric modeling technology [C]// 2nd International Conference on Computer Science and Network Technology, 2012: [14] Chen R Z, Xi P. A digraph-based hexahedral meshing method for coupled quasi-polycubes [J]. Computer Methods in Applied Mechanics and Engineering, 2014, (268): [15] Tang J, Xi P, Zhang B, et al. A finite element parametric modeling technique of aircraft wing structures [J]. Chinese

9 LI Ji-xing et al., A Turbine Blade Parametric Modeling Method Considering 1-D Heat Transfer Analysis 9 Journal of Aeronautics, 2013, 26(5): [16] Wang S T, Chi C R, Wen F B, et al. Cooling structures design for turbine blade I: Parametric Design [J]. Journal of Engineering Thermophysics, 2011, 32(4): (in Chinese). [17] Feng G T, Gu Z H, Wang Z Q, et al. Aerodynamatic design system & ideology of air-cooled turbine and its application to gas turbines [J]. Journal of Engineering Thermophysics, 2009, 30(11): (in Chinese). [18] Kan R, Chi Z R, Yang L, et al. Recent developments of gas turbine internal cooling techniques [J]. Thermal Turbine, 2013, 42(04): , 287 (in Chinese). [19] Chi C R, Wen F B, Wang S T, et al. Cooling structures design for turbine blade II: pipe-net calculation [J]. Journal of Engineering Thermophysics, 2011, 32(6): (in Chinese). [20] Fu G H, Xi P, Zhang B Y, et al. Research on heat transfer analysis data extraction for air-cooled turbine blade [J]. Journal of Graphics, 2015, 36(3): (in Chinese). [21] Yang J, Xi P, Hu B F, et al. Multi-type ribs of turbine blade modeling method fitting bowed-twist wall [J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(6): (in Chinese). LI Ji-xing is currently a Ph.D. candidate in the School of Mechanical Engineering and Automation, Beihang University. His research interests include multidisciplinary analysis oriented modeling method and geometry shape analysis. XI Ping is a professor and Ph.D. advisor at Beihang University. Her current main research interests include aircraft preliminary design and associated technologies, CAD/CAM. GUO Yan-fei is currently a graduate in the School of Software, Beihang University. Her research interests include software testing and quality management, CAGD. ZHANG Jian-qi is currently an undergraduate in the School of Mechanical Engineering, Northwestern Polytechnical University. His research interest is rapid geometric modeling method.