Fast-moving Mesh Method and Its Application to Circumferential Non-uniform Tip Clearance in a Single-stage Turbine

Document Type : Regular Article


School of Energy and Power Engineering, Beihang University, Beijing 100191, China



The circumferential non-uniform tip clearance (CNTC) due to casing out-of-roundness adversely affects the turbine aerodynamic performance due to machining and assembly errors, thermal deformation, and improper active clearance control (ACC), etc. Moreover, the asymmetric computational domain caused by casing out-of-roundness presents difficulties for conventional numerical techniques that consider rotational periodicity. Since previous traditional methods using split computational domains have the disadvantages of high interpolation error and high time cost, an efficient fast-moving mesh (FMM) method based on an algebraic approach is proposed in this paper. This method is first validated by using a single-stage turbine with elliptical casing. The results show that the FMM has the advantages of high accuracy, high efficiency, and easy operation, which helps to solve the CNTC problem quickly in scientific research or engineering applications. Then, the effects of CNTC induced by the elliptical casing on the flow field and aerodynamic performance are investigated by using an in-house code that integrates the FMM method. Finally, the effect of stator row interference on the aerodynamic performance in the turbine stage with an elliptical casing is demonstrated. The results show that different types of elliptical casings have a significant effect on the aerodynamic performance. However, the variation law is not consistent (decreasing by 0.538% or increasing by 0.212%). Importantly, the novel finding of this paper is that this discrepancy is jointly determined by the interaction of multiple secondary flows (passage vortex, scraping vortex, etc.) at different spans, not just related to the variation of the tip leakage vortex (TLV) with tip size.  Furthermore, this study is the first to indicate that the stator row interference can mitigate the extent of performance degradation due to elliptical casings by suppressing the development of secondary flows. These results may provide theoretical support for blade tip gap design and can also serve as a reasonable reference for the effective application of ACC in engineering. Finally, low-order harmonic components with high amplitudes are also innovatively found in the rotor row with a CNTC. These components may cause low-engine-order (LEO) resonances that endanger the safe operation of engines.


Main Subjects

Alford, J. S. (1965). Protecting turbomachinery from self-excited rotor whirl. Journal of Engineering for Gas Turbines and Power, 87(4), 333–343.
Allen, C. B. (2002). Aeroelastic computations using algebraic grid motion. The Aeronautical Journal106(1064), 559-570.
Benito, D., Dixon, J., & Metherell, P. (2008, January). 3D thermo-mechanical modelling method to predict compressor local tip running clearances. Turbo Expo: Power for Land, Sea, and Air.
Bunker, R. S. (2006). Axial turbine blade tips: function, design, and durability. Journal of Propulsion and Power, 22(2), 271-285.
Chen, Y., Hou, A., Wang, W., & Zhang, M. (2018). Performance estimation method for nonuniform tip clearance cases. Journal of Propulsion and Power34(6), 1355-1363.
Chen, Y., Hou, A., Zhang, M., Li, J., & Zhang, S. (2015, June). Effects of nonuniform tip clearance on fan performance and flow field. Turbo Expo: Power for Land, Sea, and Air.
De Boer, A., Van der Schoot, M. S., & Bijl, H. (2007). Mesh deformation based on radial basis function interpolation. Computers & structures85(11-14), 784-795.
DeShong, E. T., Siroka, S., Berdanier, R. A., & Thole, K. A. (2022). Evaluating the influence of rotor-casing eccentricity on turbine efficiency including time-resolved flow field measurements. Journal of Turbomachinery144(2), 021012.
Erhard, J., & Gehrer, A. (2000, May). Design and construction of a transonic test-turbine facility. Turbo Expo: Power for Land, Sea, and Air.
G ttlich, E., Neumayer, F., Woisetschl ger, J., Sanz, W., & Heitmeir, F. (2004). Investigation of stator-rotor interaction in a transonic turbine stage using laser doppler velocimetry and pneumatic probes. Journal of Turbomachinery126(2), 297-305.
Gaffin, W. O. (1979). JT9D-70/59 Improved high pressure turbine active clearance control system (No. NASA-CR-159661).
Gaitonde, A. L., & Fiddes, S. P. (1995). A three-dimensional moving mesh method for the calculation of unsteady transonic flows. The Aeronautical Journal99(984), 150-160.
Gaitonde, A., & Fiddes, S. (1993, January). A moving mesh system for the calculation of unsteady flows. 31st Aerospace Sciences Meeting.
Hu, J. L., Gao, J. H., Liu, G., Cui, L., & Guo, B. T. (2018). Experiment of high pressure turbine case based on active clearance control system. Journal of Propulsion Technology, 39(4), 740-750.
Jameson, A. (1991, June). Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. 10th Computational fluid dynamics conference.
Jiang, C., Hu, J., Wang, J., & Cong, L. (2020). Numerical investigation on flow field distribution of eccentric compressors based on steady and unsteady cfd methods. Energies13(22), 6081.
Lattime, S. B., & Steinetz, B. M. (2004). High-pressure-turbine clearance control systems: current practices and future directions. Journal of Propulsion and Power20(2), 302-311.
Lavagnoli, S., De Maesschalck, C., & Andreoli, V. (2017). Design considerations for tip clearance control and measurement on a turbine rainbow rotor with multiple blade tip geometries. Journal of Engineering for Gas Turbines and Power139(4), 042603.
Liu, Y., Tan, L., & Wang, B. (2018). A review of tip clearance in propeller, pump and turbine. Energies11(9), 2202.
Melcher, K. J., & Kypuros, J. A. (2003, December). Toward a fast-response active turbine tip clearance control. 16th International Symposium on Airbreathing Engines (No. E-14185).
Menter, F. R. (1993, July). Zonal two equation kw turbulence models for aerodynamic flows. 23rd fluid dynamics, plasmadynamics, and lasers conference.
Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal32(8), 1598-1605.
Olsson, W. J., & Martin, R. L. (1982). B747/JT9D flight loads and their effect on engine running clearances and performance deterioration; BCAC NAIL/P and WA JT9D engine diagnostics programs (No. NAS 1.26: 165573).
Pan, Y., Yuan, Q., Huang, G., Gu, J., Li, P., & Zhu, G. (2020). Numerical investigations on the blade tip clearance excitation forces in an unshrouded turbine. Applied Sciences10(4), 1532.
Reuther, J., Jameson, A., Farmer, J., Martinelli, L., & Saunders, D. (1996, January). Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation. 34th aerospace sciences meeting and exhibit.
Roe, P. L. (1981). Approximate riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics43(2), 357-372.
Song, S. J. (1998). Inviscid rotordynamic damping forces due to nonaxisymmetric tip clearance in turbines. AIAA Journal36(12), 2163-2169.
Song, S. J., & Martinez-Sanchez, M. (1997a). Rotordynamic forces due to turbine tip leakage: Part I—blade scale effects. Journal of Turbomachinery, 119(4), 695–703.
Song, S. J., & Martinez-Sanchez, M. (1997b). Rotordynamic forces due to turbine tip leakage: Part II—radius scale effects and experimental verification. Journal of Turbomachinery. 119(4), 704–713.
Zhang, L. P. (2010). Reviews of moving grid generation techniques and numerical methods for unsteady flow. Advances in Mechanics, 40(4), 424-447.
Zheng, Y. (2004). Computational aerodynamics on unstructed meshes [Doctoral dissertation, Durham University].
Zheng, Y., & Yang, H. (2011). Coupled fluid-structure flutter analysis of a transonic fan. Chinese Journal of Aeronautics24(3), 258-264.
Zheng, Y., & Yang, H. (2013). Full assembly fluid/structured flutter analysis of a transonic fan. Journal of Beijing University of Aeronautics and Astronautics39(5), 626-630.
Zheng, Y., Jin, X., & Yang, H. (2022). Effects of asymmetric vane pitch on reducing low-engine-order forced response of a turbine stage. Aerospace9(11), 694.
Zheng, Y., Jin, X., Yang, H., Gao, Q., & Xu, K. (2020, September). Effects of circumferential nonuniform tip clearance on flow field and performance of a transonic turbine. Turbo Expo: Power for Land, Sea, and Air. American Society of Mechanical Engineers.
Zheng, Y., Wang, B., Wang, J., & Xiao, D. (2012). Mesh deforming technique based on compatibility of multi-block structured mesh deformation and its application to blade aerodynamic analysis in turbomachinery. Aeronautical Computing Technique42, 83-87.