Parametric construction of blade leading and trailing edges with arbitrary central angles using NURBS curves

NI Haonan; XU Jingchao; XIA Yifan; CHEN Jianjun

doi:10.7638/kqdlxxb-2025.0130

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Parametric construction of blade leading and trailing edges with arbitrary central angles using NURBS curves

更新时间：2026-05-28

- Parametric construction of blade leading and trailing edges with arbitrary central angles using NURBS curves
- Vol. 43, Issue 8, Pages: 130-142(2025)
- 作者机构：
  
  浙江大学航空航天学院,杭州,310027
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2025.0130
  CLC： O242
- Published：2025
- 稿件说明：
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倪浩楠, 徐璟潮, 夏一帆, 等. 基于NURBS曲线的任意圆心角度叶型前尾缘构造[J]. 空气动力学学报, 2025, 43(8): 130−142.

NI Haonan, XU Jingchao, XIA Yifan, et al. Parametric construction of blade leading and trailing edges with arbitrary central angles using NURBS curves[J]. 2025, 43(8): 130-142.
倪浩楠, 徐璟潮, 夏一帆, 等. 基于NURBS曲线的任意圆心角度叶型前尾缘构造[J]. 空气动力学学报, 2025, 43(8): 130−142. DOI： 10.7638/kqdlxxb-2025.0130

NI Haonan, XU Jingchao, XIA Yifan, et al. Parametric construction of blade leading and trailing edges with arbitrary central angles using NURBS curves[J]. 2025, 43(8): 130-142. DOI： 10.7638/kqdlxxb-2025.0130.

摘要

具有良好灵活性的叶型前尾缘构造方法对于叶轮机械的叶型设计和优化至关重要。本文研究了一种在经典 NURBS 表示框架下，结合圆锥截线和圆弧几何特性，实现叶片前缘与尾缘的多自由度构造方法。该方法在叶栅气动弦长基本不变、保证补圆曲线与叶盆、叶背曲线在连接处的 G

连续性的前提下，通过少量参数灵活调节圆锥截线的斜度、锥度和尺寸，实现对前缘和尾缘形状的有效控制。基于补圆类型及圆心角信息，求解控制点和权因子，精确构造任意圆心角度满足凸包性要求的圆锥截线。此外，将补圆参数与展向叶型截面数相关联，实现补圆几何随展向的动态变化，完成三维叶片复杂前尾缘的高效参数化建模。数值模拟表明，与原始叶型相比，采用本文方法构造前尾缘的跨声速叶片具有更高的等熵压缩效率，且前缘区域的激波强度明显减弱。

Abstract

A highly flexible method for constructing the leading and trailing edges of airfoils plays a significant role in the design and optimization of turbomachinery blade profiles. This paper investigates a multi-degree-of-freedom approach for shaping the leading and trailing edges based on the classical NURBS representation framework

incorporating the geometric characteristics of conic sections and circular arcs. The proposed method enables effective control over the leading and trailing edge profiles by flexibly adjusting the slope

taper

and size of the conic section using only a few parameters

while maintaining the ae

rodynamic chord length of the blade row and ensuring G

continuity at the junctions between the fillet curves and the suction/pressure side curves. Control points and weights are computed based on the specified fillet type and central angle to precisely construct conic sections satisfying convex hull requirements. Furthermore

the fillet parameters are linked to the number of blade sections along the spanwise direction

allowing for dynamic variation of the fillet geometry and enabling efficient parametric modeling of complex 3D blade leading and trailing edges. Numerical simulations demonstrate that

compared with the original airfoil

transonic blades incorporating the proposed edge construction method exhibit significantly improved isentropic compression efficiency and a noticeable weakening of shock waves in the leading-edge region.

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references

PAPILA N, SHYY W, GRIFFIN L, et al. Shape optimization of supersonic turbines using response surface and neural network methods[C]// 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA: AIAA, 2001. doi: 10.2514/6.2001-1065

LEE S Y, KIM K Y. Design optimization of axial flow compressor blades with three-dimensional Navier-Stokes solver[J]. KSME International Journal, 2000, 14(9): 1005−1012. doi: 10.1007/BF03185803

GOODHAND M N, MILLER R J. Compressor leading edge spikes: A new performance criterion[J]. Journal of Turbomachinery, 2011, 133(2): 021006. doi: 10.1115/1.4000567

WHEELER A P S, SOFIA A, MILLER R J. The effect of leading-edge geometry on wake interactions in compressors[J]. Journal of Turbomachinery, 2009, 131(4): 041013. doi: 10.1115/1.3104617

LU H Z, XU L P, FANG R. Improvement of compressor blade leading edge design[J]. Journal of Aerospace Power, 2000, 15(2): 129−132 (in Chinese). doi: 10.3969/j.issn.1000-8055.2000.02.004

YANG G H, GAO L M, WANG H H, et al. Asymmetric leading edge design of diffusion cascade based on NURBS[J]. Journal of Aerospace Power, 2021, 36(3): 655−663 (in Chinese).

SALUNKE N P, CHANNIWALA S A. Design and analysis of a controlled diffusion aerofoil section for an axial compressor stator and effect of incidence angle and Mach No. on performance of CDA[J]. International Journal of Fluid Machinery and Systems, 2010, 3(1): 20−28. doi: 10.5293/ijfms.2010.3.1.020

BEHLKE R F. The development of a second-generation of controlled diffusion airfoils for multistage compressors[C]// ASME 1985 Beijing International Gas Turbine Symposium and Exposition, 2015. doi: 10.1115/85-IGT-9

HOBBS D E, WEINGOLD H D. Development of controlled diffusion airfoils for multistage compressor application[J]. Journal of Engineering for Gas Turbines Power, 1984, 106(2): 271−278. doi: 10.1115/1.3239559

JIN J, LIU B, NAN X Y, et al. Influence effect of supersonic airfoil’s leading edge geometric shape on aero-dynamical performance of cascade[J]. Journal of Aerospace Power, 2007, 22(4): 660-665 (in Chinese).

LI Z J, ZOU J G, WANG S M, et al. Research on parametric modeling method of high subsonic compressor blade profile based on NURBS curve[J]. Journal of Engineering for Thermal Energy and Power, 2022, 37(12): 29-37 (in Chinese).

YANG J, NING T, XI P. Geometric design of leading edge with specified curvature at leading edge point[J]. Journal of Computer-Aided Design Computer Graphics, 2016, 28(7): 1195−1200 (in Chinese). doi: 10.3969/j.issn.1003-9775.2016.07.021

ZHANG J H, ZHOU Z G, WEI W Q, et al. Aerodynamic design of an ultra-low rotating speed geared fan[J]. Aerospace Science and Technology, 2017, 63: 73−81. doi: 10.1016/j.ast.2016.12.024

MOHAMMED K P, RAJ D P. Investigations on axial flow fan impellers with forward swept blades[J]. Journal of Fluids Engineering, 1977, 99(3): 543−547. doi: 10.1115/1.3448839

GALLIMORE S J, BOLGER J J, CUMPSTY N A, et al. The use of sweep and dihedral in multistage axial flow compressor blading: part II: Low and high-speed designs and test verification[J]. Journal of Turbomachinery, 2002, 124(4): 533−541. doi: 10.1115/1.1507334

VOß C, SIGGEL M, BACKHAUS J, et al. A differentiated geometry blade parameterization methodology for gas turbines[J]. Computers Fluids, 2025, 292: 106588. doi: 10.1016/j.compfluid.2025.106588

YUAN H, WU Y F, ZHANG J S, et al. Integrated optimization of a turbine stage at a low Reynolds number via NURBS surface and machine learning[J]. Energy, 2024, 294: 130956. doi: 10.1016/j.energy.2024.130956

YANG G, GAO L, MA C, et al. Investigation on aerodynamic robustness of compressor blade with asymmetric leading edge[J]. Journal of Applied Fluid Mechanics, 2024, 17(2). doi: 10.47176/jafm.17.02.2127

PIEGL L A, TILLER W. The NURBS book[M]. Springer Berlin Heidelberg, 1997.

SCHAEFER S, WARREN J, ZORIN D. Lofting curve networks using subdivision surfaces[C]//Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, Nice France. ACM, 2004. doi: 10.1145/1057432.1057447

ZHENG R Y, XIANG J H, SUN J J. Blade geometry optimization for axial flow compressor[C]// Proceedings of the ASME Turbo Expo, Volume 7: 633-644, Glasgow, UK. ASMEDC, 2010. doi: 10.1115/gt2010-22229

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