June  2020, 28(2): 837-851. doi: 10.3934/era.2020043

Numerical simulation for 3D flow in flow channel of aeroengine turbine fan based on dimension splitting method

1. 

School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China

2. 

Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences, Shenzhen 518055, China

3. 

Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China

4. 

School of Science, Xi'an Jiaotong University, Xi'an 710049, China

5. 

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

* Corresponding authors

Received  December 2019 Revised  March 2020 Published  May 2020

In this paper, we introduce a dimension splitting method for simulating the air flow state of the aeroengine turbine fan. Based on the geometric model of the fan blade, the dimension splitting method establishes a semi-geodesic coordinate system. Under such coordinate system, the Navier-Stokes equations are reformulated into the combination of membrane operator equations on two-dimensional manifolds and bending operator equations along the hub circle. Using Euler central difference scheme to approximate the third variable, the new form of Navier-Stokes equations is splitting into a set of two-dimensional sub-problems. Solving these sub-problems by alternate iteration, it follows an approximate solution to Navier-Stokes equations. Furthermore, we conduct a numerical experiment to show that the dimension splitting method has a good performance by comparing with the traditional methods. Finally, we give the simulation results of the pressure and flow state of the fan blade.

Citation: Guoliang Ju, Can Chen, Rongliang Chen, Jingzhi Li, Kaitai Li, Shaohui Zhang. Numerical simulation for 3D flow in flow channel of aeroengine turbine fan based on dimension splitting method. Electronic Research Archive, 2020, 28 (2) : 837-851. doi: 10.3934/era.2020043
References:
[1]

P. G. Ciarlet, An introduction to differential geometry with applications to elasticity, Journal of Turbomachinery, 78 (2005), 1-215.  doi: 10.1007/s10659-005-4738-8.  Google Scholar

[2]

J. DeCastro, J. Litt and D. Frederick, A modular aero-propulsion system simulation of a large commercial aircraft engine, 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, (2008), 4579. doi: 10.2514/6.2008-4579.  Google Scholar

[3]

N. J. Georgiadis and J. R. DeBonis, Navier-Stokes analysis methods for turbulent jet flows with application to aircraft exhaust nozzles, Progress in Aerospace Sciences, 42 (2006), 377-418.  doi: 10.1016/j.paerosci.2006.12.001.  Google Scholar

[4]

I. K. Jennions and M. G. Turner, Three-dimensional navier-stokes computations of transonic fan flow using an explicit flow solver and an implicit solver, Journal of Elasticity, 115 (1993), 261-272.  doi: 10.1115/1.2929232.  Google Scholar

[5] K. Li and A. Huang, Navier-Stokes Boundary Shape Control, Dimension Splitting Method and its Application(in Chinese), 1nd ed., Science Press, Beijing, 2013.   Google Scholar
[6]

G. JuJ. Li and K. Li, A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry, Applicable Analysis, 1 (2019), 1-17.  doi: 10.1080/00036811.2018.1559304.  Google Scholar

[7]

N. Nekoubin and Mrh. Nobari, Numerical investigation of transonic flow over deformable airfoil with plunging motion, Applied Mathematics and Mechanics, 37 (2016), 75-96.  doi: 10.1007/s10483-016-2019-9.  Google Scholar

[8] B. O'neill, Semi-Riemannian Geometry with Applications to Relativity, Academic press, alt Lake, 1983.   Google Scholar
[9]

H. Schlichting and K. Gersten, Boundary-layer Theory, 9nd ed., Springer, Berlin, 2016. Google Scholar

[10]

K. TakizawaT. E. Tezduyar and H. Hattori, Computational analysis of flow-driven string dynamics in turbomachinery, Computers Fluids, 142 (2017), 109-117.  doi: 10.1016/j.compfluid.2016.02.019.  Google Scholar

[11]

J. C. TyackeM. Mahak and P. G. Tucker, Large-scale multifidelity, multiphysics, hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation of an installed aeroengine, Journal of Propulsion and Power, 1 (2016), 997-1008.  doi: 10.2514/1.B35947.  Google Scholar

[12]

H. Xuan and R. Wu, Aeroengine turbine blade containment tests using high-speed rotor spin testing facility, Aerospace Science and Technology, 10 (2006), 501-508.  doi: 10.1016/j.ast.2006.04.006.  Google Scholar

[13]

J. Yeuan, T. Liang and A. Hamed, A 3-D Navier-Stokes solver for turbomachinery blade rows, 32nd Joint Propulsion Conference and Exhibit, (1996), 3308. doi: 10.2514/6.1996-3308.  Google Scholar

[14]

Z. YunW. Biao and Y. Hui, Numerical study on blade un-running design of a transonic fan, Journal of Mechanical Engineering, 49 (2013), 147-153.   Google Scholar

[15]

K. ZhangM. Li and J. Li, Estimation of impacts of removing arbitrarily constrained domain details to the analysis of incompressible fluid flows, Communications in Computational Physics, 20 (2016), 944-968.  doi: 10.4208/cicp.071015.050216a.  Google Scholar

[16]

J. ZhangK. ZhangJ. Li and X. Wang, A weak Galerkin finite element method for the Navier-Stokes equations, Communications in Computational Physics, 23 (2018), 706-746.  doi: 10.4208/cicp.oa-2016-0267.  Google Scholar

show all references

References:
[1]

P. G. Ciarlet, An introduction to differential geometry with applications to elasticity, Journal of Turbomachinery, 78 (2005), 1-215.  doi: 10.1007/s10659-005-4738-8.  Google Scholar

[2]

J. DeCastro, J. Litt and D. Frederick, A modular aero-propulsion system simulation of a large commercial aircraft engine, 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, (2008), 4579. doi: 10.2514/6.2008-4579.  Google Scholar

[3]

N. J. Georgiadis and J. R. DeBonis, Navier-Stokes analysis methods for turbulent jet flows with application to aircraft exhaust nozzles, Progress in Aerospace Sciences, 42 (2006), 377-418.  doi: 10.1016/j.paerosci.2006.12.001.  Google Scholar

[4]

I. K. Jennions and M. G. Turner, Three-dimensional navier-stokes computations of transonic fan flow using an explicit flow solver and an implicit solver, Journal of Elasticity, 115 (1993), 261-272.  doi: 10.1115/1.2929232.  Google Scholar

[5] K. Li and A. Huang, Navier-Stokes Boundary Shape Control, Dimension Splitting Method and its Application(in Chinese), 1nd ed., Science Press, Beijing, 2013.   Google Scholar
[6]

G. JuJ. Li and K. Li, A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry, Applicable Analysis, 1 (2019), 1-17.  doi: 10.1080/00036811.2018.1559304.  Google Scholar

[7]

N. Nekoubin and Mrh. Nobari, Numerical investigation of transonic flow over deformable airfoil with plunging motion, Applied Mathematics and Mechanics, 37 (2016), 75-96.  doi: 10.1007/s10483-016-2019-9.  Google Scholar

[8] B. O'neill, Semi-Riemannian Geometry with Applications to Relativity, Academic press, alt Lake, 1983.   Google Scholar
[9]

H. Schlichting and K. Gersten, Boundary-layer Theory, 9nd ed., Springer, Berlin, 2016. Google Scholar

[10]

K. TakizawaT. E. Tezduyar and H. Hattori, Computational analysis of flow-driven string dynamics in turbomachinery, Computers Fluids, 142 (2017), 109-117.  doi: 10.1016/j.compfluid.2016.02.019.  Google Scholar

[11]

J. C. TyackeM. Mahak and P. G. Tucker, Large-scale multifidelity, multiphysics, hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation of an installed aeroengine, Journal of Propulsion and Power, 1 (2016), 997-1008.  doi: 10.2514/1.B35947.  Google Scholar

[12]

H. Xuan and R. Wu, Aeroengine turbine blade containment tests using high-speed rotor spin testing facility, Aerospace Science and Technology, 10 (2006), 501-508.  doi: 10.1016/j.ast.2006.04.006.  Google Scholar

[13]

J. Yeuan, T. Liang and A. Hamed, A 3-D Navier-Stokes solver for turbomachinery blade rows, 32nd Joint Propulsion Conference and Exhibit, (1996), 3308. doi: 10.2514/6.1996-3308.  Google Scholar

[14]

Z. YunW. Biao and Y. Hui, Numerical study on blade un-running design of a transonic fan, Journal of Mechanical Engineering, 49 (2013), 147-153.   Google Scholar

[15]

K. ZhangM. Li and J. Li, Estimation of impacts of removing arbitrarily constrained domain details to the analysis of incompressible fluid flows, Communications in Computational Physics, 20 (2016), 944-968.  doi: 10.4208/cicp.071015.050216a.  Google Scholar

[16]

J. ZhangK. ZhangJ. Li and X. Wang, A weak Galerkin finite element method for the Navier-Stokes equations, Communications in Computational Physics, 23 (2018), 706-746.  doi: 10.4208/cicp.oa-2016-0267.  Google Scholar

Figure 1.  Aeroengine turbine fan
Figure 2.  Channel between two adjacent blades
Figure 3.  The channel of impellers when $ \Theta = 0 $
Figure 4.  One of blade in R-coordinate system
Figure 5.  The mesh of central surface generated by different methods
Figure 6.  The comparisons of velocity magnitude calculated by different methods
Figure 7.  The comparisons of velocity $ u_1 $ calculated by different methods
Figure 8.  The comparisons of velocity $ u_2 $ calculated by different methods
Figure 9.  The comparisons of velocity $ u_3 $ calculated by different methods
Figure 10.  The comparisons of Pressure calculated by different methods
Figure 11.  The pressure distribution of positive pressure surface
Figure 12.  The pressure distribution of negative pressure surface
Figure 13.  The 3D model of pressure distribution of positive pressure surface
Figure 14.  The 3D model of pressure distribution of negative pressure surface
Figure 15.  The blade mesh in R-coordinate system
Figure 16.  Velocity distribution at outlet
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