第五章 結論與未來研究方向
5.2 建議
由上述的結論中雖然可知本研究葉片參數之最佳化設計，但因影響幫浦 性能的因子很多，但本研究中參數模型之數值模擬僅針對葉片入口角、葉片
出口角及葉片數等三種參數之組合作分析，故提出以下之建議，希望未來的 研究整合，能在設計階段即配合數值模擬分析，開發出更符合需求及性能再 提昇的理想幫浦。
1.擴大本研究葉片參數數值之範圍，如葉片入口角與出口角度可以由10°增 加到80°，葉片數可由4片改變至8片，增加參數模型組合，並配合田口法 作最佳化設計。
2.增加文獻中對幫浦性能影響較大之設計參數，如增加葉片入口直徑D1、 葉片入口寬度b1、葉片出口寬度b2及葉片厚度S等參數，並配合田口法作 最佳化設計。
3.分析不同轉速對離心式水幫浦性能的影響，期望找出最佳之運轉條件。
4.本研究僅限定於流場之模擬，並未考慮葉片結構性問題，未來可利用ADINA 軟體在多重物理耦合的強大功能性，於流固區間各使用不同的網格，及 在界面用不吻合網格(Dis-similar Mesh)，分析幫浦內葉片之真實雙向 流固耦合(FSI)。
5.針對參數模型之設計，是否因葉片之形狀及數目改變，導致固定轉速下驅 動葉輪之動力需求增加，可以加入功率與效率之探討，作為未來幫浦選 用考量之一。
參考文獻
1. Church, G., “Centrifugal Pump and Blowers,” Wiley, New York, 1944.
2. Stepanoff, A. J., “Centrifugal and Axial Flow Pumps,” Wiley, New York, 1957.
3. Tuzson, J., “Centrifugal Pump Design,” Wiley, New York, 2000.
4. Eck, B., “Fans”, Pergamon Press, N. Y. , 1975.
5. Raj, D., “Identification of Noise Sources in Forward-Curved Centrifugal Fan Rotors”, Tennessee Technological University, Ph. D. Thesis, Cookeville, Tennessee, 1978.
6. Eckardt, D., “Instantaneous Measurements in the Jet-Wake Discharge Flow of a Centrifugal Compressor Impeller”, ASME Journal of Engineering for
Power, Vol. 97, pp.337-346, 1975.
7.神宮 敬, “泵之設計製圖＂, 台隆書店出版, 1982.
8.蘇宗寶, “離心式泵”, 徐氏基金會出版, 1986.
9. Zhang, M. J., Pomfret, M. J., and Wong, C. M., “Three-Dimensional Viscous Flow Simulation in a Backswept Centrifugal Impeller at the Design Point,”
Computers & Fluids, vol. 25, No. 5, pp.497-507, 1996.
10. Pierret, S., “Turbomachinery Blade Design Using a Navier-Stokes Solver and Artificial Neural Network,” Transactions of the ASME Journal of Turbomachinery, vol. 121, 1998.
11. Ardizzon, G. and Pavesi, G.., “Optimum Incidence Angle in Centrifugal Pumps and Radial Inflow Turbines, ” Proceedings of the Institution of Mechanical Engineers, vol. 212-part A, pp.97-107, 1998.
12. Jude, L. and Homentcovschi, D., “Numerical Analysis of the Inviscid Incompressible Flow in Two-Dimensional Radial-Flow Pump Impellers”, ELSEVIER, Engineering Analysis with Boundary Elements, Vol. 22, pp.271-279, 1998.
13. Oh, H. W., and Chung, M. K., “Optimum Values of Design Variables versus Specific Speed for Centrifugal Pumps”, Proceedings of the Institution of Mechanical Engineers-A-Journal of Power and Energy, Vol. 213, pp.219-226, 1999.
14. Su, S. P., Chen, S. H., Lee, L. C., and Hwang, T. Y., The Use of CFD in Turbomachinery Applications, ” Transactions of the Aeronautical and
Astronautical Society of the Republic of China, vol. 32, No. 1, pp.1-24, 2000.
15. S. S. Hong and S. S. Kang, “Flow at the Centrifugal Pump Impeller Exit With Circumferential Distortion of the Outlet Static Pressure, ” Transactions of ASME, Journal of Fluids Engineering, vol. 124, pp.314-318, 2002.
16. Goto, A. and Zangendh, M. “Hydrodynamic Design of Pump Diffuser Using Inverse Design Method and CFD, ” Transactions of ASME, Journal of Fluids Engineering, vol. 124, pp. 319-328, 2002.
17. Goto, A., Nohmi, M., Sakurai, T. and Sogawa, Y., “Hydrodynamic Design System for Pumps Based on 3-D CAD, CFD, and Inverse Design Method,”
Transactions of ASME, Journal of Fluids Engineering, vol. 124, pp.329-335, 2002.
18. Song, X., G. H. Wood and Olsen, D., “Computational Fluid Dynamics (CFD)Study if the 4th Generation Prototype of a Continuous Flow Ventricular Assist Device(VAD), ” Transactions of ASME, Journal of Biomechanical Engineering, vol. 126, pp.180-187, 2004.
19.劉鼎嶽, “機械設計製圖”, 新文京開發出版股份有限公司, 2007.
20.袁壽其, “低比速離心泵理論與設計”, 機械工業出版社, 1997.
21.余國全, “葉片出口角對後傾離心泵的性能影響之數值研究”, 國立台灣科 技大學碩士學位論文, 2005.
附錄一、ADINA 數值設定
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附錄二、ADINA 軟體驗證
【ADINA 8.5.3 Verification & Validation】
COMPUTER HARDWARE VERIFICATION SUMMARY Title of Program: ADINA
Revision/Version: 8.5.3 Origin of Program:
ADINA was developed and marketed by ADINA, Inc.
Brief Description of Program:
The ADINA computer program is a large-scale general purpose Finite Element computer program for the solution of several classes of engineering analyses that include: static, dynamic, structure-related-thermal analyses.
Tested for Which Application:
The code was verified for its structural, structure-related-thermal analysis capabilities.
Method Used to Verify Program:
Test problems were selected from the ADINA Version 8.5.3 Verification Manual and run on ASUS computers operating on Microsoft Windows XP. Results were compared to ADINA results in the ADINA Verification Manual.
References/Documents to Support Verification/Validation:
ADINA Revision 8.5.3 Verification Manual.
Title of User's Manual:
ADINA Revision 8.5.3 Users Manual.
Description of Benchmark Tests/Alternate Calculations:
Tests are performed from test cases in the ADINA Verification Manual. In general, the processes of benchmark follow steps being conducted by XXX for the similar benchmark, which is in compliance with the requirement of NUREG/CR-6608.
F.1 General Couette flow (2-D and 3-D elements)
Objective
To verify the behavior of the two- and three-dimensional quadratic fluid flow elements.
Physical problem
The problem of the general Couette flow is considered, see Fig. F.1. The bottom surface is fixed and the top surface is moving at a constant velocity. There is also a pressure gradient applied in the flow direction. The flow is assumed to be a fully developed laminar flow and the velocity profile is to be found.
Finite element model
This problem is solved using two separate two- and three-dimensional models in the same analysis. In each model three quadratic elements are used normal to the flow direction. A steady-state flow condition is assumed.
References
[1] Schlichting, H., Boundary-Layer Theory, 7th edition, McGraw-Hill Company, New York, 1979.
[2]Potter, M.C. and Foss, J.F., Fluid Mechanics, The Ronald Press Company, 1975.
Results Comparison
2-D
Target ADINA Ratio
velocity z=0 0 0 1
z=1 120 120 1
z=2 140 140 1
z=3 60 60 1
shear stress z=0 1.7 1.7 1
z=1 0.7 0.7 1
z=2 -0.3 -0.3 1
z=3 -1.3 -1.3 1
3-D
Target ADINA Ratio
velocity z=0 0 0 1
z=1 120 120 1
z=2 140 140 1
z=3 60 60 1
shear stress z=0 1.7 1.7 1
z=1 0.7 0.7 1
z=2 -0.3 -0.3 1
z=3 -1.3 -1.3 1
F.2 Flow in a pipe (axisymmetric elements)
Objective
To verify the behavior of the 4-node axisymmetric FCBI elements.
Physical problem
The problem of a fully developed flow in a pipe is considered, see Fig. F.2. A pressure gradient is applied in the axial direction, and the velocity profile is to be found.
Finite element model
The finite element model consists of 4-node axisymmetric FCBI elements. The pressure gradient is imposed by applying a uniform pressure of 10 on the left face and no pressure on the right face. A steady-state flow condition is assumed.
Reference
[1]Potter, M.C. and Foss, J.F., Fluid Mechanics, The Ronald Press Company, 1975.
Results Comparison
Target ADINA Ratio
velocity z =-2 0 0 1
z =-1 3.75 3.75 1
z =0 5 5 1
z =1 3.75 3.75 1
z =2 0 0 1
shear stress z=-2 1 0.9688 1.0322
z=-1 0.5 0.4667 1.0735
z =0 0 0.03122 1
z =1 -0.5 -0.4667 1.0735
z =2 -1 -1 1
F.5 Laminar flow between rotating cylinders
Objective
To verify the behavior of the 4-node two-dimensional FCBI elements.
Physical problem
The problem of a fully developed flow between concentrically rotating cylinders is considered, as shown in Fig. F.5. Body force effects are ignored.
Finite element model
The finite element model consists of 4-node 2-D FCBI elements.
The inner and outer rotating cylinders are modeled with an angular velocity boundary condition.
The pressure at one point on the inner cylinder is set to zero.
Reference
[1]Potter, M.C. and Foss, J.F., Fluid Mechanics, The Ronald Press Company, 1975.
Results Comparison
Target ADINA Ratio
velocity r=1.0 1 1 1.0000
r=1.2 1.6888 1.67544 0.9921
r=1.4 2.314 2.29219 0.9906
r=1.6 2.899 2.87513 0.9918
r=1.8 3.45925 3.4404 0.9946
r=2.0 4 4 1.0000 shear stress r=1.0 2.66 2.64530E+00 0.9945
r=1.2 1.85185 1.8727 1.0113
r=1.4 1.360544 1.37492E+00 1.0106
r=1.6 1.04167 1.05459E+00 1.0124
r=1.8 0.823045 8.38376E-01 1.0186
r=2.0 0.75 7.12536E-01 0.9500
pressure r=1.0 0 6.46164E-13 ≒0
r=1.2 0.33493 3.29469E-01 0.9837
r=1.4 0.955102 9.48788E-01 0.9934 r=1.6 1.863866 1.85584E+00 0.9957
r=1.8 3.05497 3.04495E+00 0.9967
r=2.0 4.5266 4.46264E+00 0.9859
vorticity r=1.0 -4.66667 -4.64745E+00 1.0041 r=1.2 -4.66667 -4.65796E+00 1.0019 r=1.4 -4.66667 -4.66847E+00 0.9996 r=1.6 -4.66667 -4.67898E+00 0.9974 r=1.8 -4.66667 -4.68949E+00 0.9951 r=2.0 -4.66667 -4.70000E+00 0.9929
F.7 Non-Newtonian flow between two parallel plates (2-D and 3-Delements)
Objective
To verify the fluid power law material model for the quadratic 2-D and 3-D fluid elements.
Physical problem
The laminar steady flow of a non-Newtonian fluid between two parallel plates is considered, see Fig. F.7. A pressure gradient is applied in the flow direction. The velocity profile is to be found.
Finite element model
This problem is solved using two separate two-and three-dimensional models in the same analysis. Due to symmetry, only one half of the fluid flow is considered. The finite element model consists of 9-node 2-D elements and 27-node 3-D elements, with five elements in the z direction. The power law fluid model is used to represent the non-Newtonian fluid.
Reference
[1]Crochet, M.J., Davies, A.R. and Walters, K., Numerical Simulation of Non-Newtonian Flow, Elsevier, New York and Amsterdam, 1983.
Results Comparison
Target ADINA Ratio
velocity z=0 0 0.00000E+00 1
z=0.1 1.4856E-03 1.48162E-03 1.0026 z=0.2 2.0379E-03 2.03262E-03 1.0026 z=0.3 2.18708E-03 2.18153E-03 1.0025 z=0.4 2.20900E-03 2.20521E-03 1.0017 z=0.5 2.20970E-03 2.21021E-03 0.99977 shear stress z=0 0.5 4.96012E-01 1.008
z=0.1 0.4 3.96134E-01 1.0097
z=0.2 0.3 2.95234E-01 1.016
z=0.3 0.2 1.93568E-01 1.033
z=0.4 0.1 8.55853E-02 1.167
z=0.5 0 0.00000E+00 1
F.9 No flow test
Objective
To verify the behavior of the 4-node 2-D FCBI elements when subjected to gravity loading.
Physical problem
The fluid in the domain shown in Fig. F.9 is subjected to gravity loading. Zero velocities are imposed on the fluid boundaries, and the solution should of course give zero velocities
everywhere and a hydrostatic pressure distribution.
Finite element model
The finite element model consists of 72 4-node 2-D FCBI elements. The pressure is assumed to be zero at one node on the top surface (z = 0) and gravity loading is applied.
Reference
[1] Fortin, M. and Fortin, A., "Experiments with Several Elements for Viscous
Incompressible Flows," Int. J. for Numerical Methods in Fluids, Vol. 5, pp. 911-928,1985.
Results Comparison
Target ADINA Ratio
velocity z=0 0 0.00000E+00 1
z=-5 0 0.00000E+00 1
z=-10 0 0.00000E+00 1
z=-15 0 0.00000E+00 1
z=-20 0 0.00000E+00 1
pressure z=0 0 0.00000E+00 1
z=-5 50 5.00000E+01 1
z=-10 100 1.00000E+02 1
z=-15 150 1.50000E+02 1
z=-20 200 2.00000E+02 1
F.33 Sinusoidal oscillation of a flat plate supporting a fluid
Objective
To verify the use of the restart option and the assignment of initial conditions in transient analysis using 4-node 2-D FCBI elements.
Physical problem
An infinite flat plate is supporting a fluid and oscillating sinusoidally, see Fig. F.33. The velocity profile of the fluid is to be determined.
Finite element model
The finite element model consists of forty 4-node 2-D FCBI elements. The Euler backward time integration method with a time increment t△ =2π/80 is used for a total of 80 time steps.
Two consecutive runs are made. The first run consists of 40 time steps which correspond to the time span 0 to π. The second run using the restart option consists of another 40 time steps which correspond to the time span from π to
2π. Initial velocities obtained from the analytical solution are assigned to all nodes for the first run.
Reference
[1] Potter, M.C.and Foss, J.F., Fluid Mechanics, The Ronald Press Company, New York, p. 289, 1975
Results Comparison
Target ADINA Ratio
velocity z=0 1 1.00000E+00 1
z= ∞ 0 0.00000E+00 1
F.35 Heat generated in laminar flow between two rotating cylinders (2- D elements)
Objective
To verify the behavior of the 4-node axisymmetric FCBI elements, in particular the calculation of viscous dissipation.
Physical problem
The problem of a fully developed flow between two concentrically rotating cylinders is considered. The same problem is also considered in Example F.5 but without viscous dissipation. Here θ1 = 0, θ2 = 1 and k = 0.2, corresponding to a Brinkman number of 5, see below.
Finite element model
The finite element model is the same as in Example F.5, except that viscous dissipation is considered.
Reference
[1] White, F.M., Viscous Fluid Flow, McGraw-Hill Book Company, New York, p. 117,1974.
Results Comparison
Target ADINA Ratio
velocity r=1.0 1 1 1.00
r=1.2 1.6888 1.67544 0.99
r=1.4 2.314 2.29219 0.99
r=1.6 2.899 2.87513 0.99
r=1.8 3.45925 3.4404 0.99
r=2.0 4 4 1.00 temperature r=1.0 0 2.64530E+00 0.99
r=1.2 1.38895 1.01
r=1.4 1.7456 1.01
r=1.6 1.65894 1.01
r=1.8 1.37343 1.02
r=2.0 0.95
F.37 Free-convection flow between two vertical plates (2-D elements)
Objective
To verify the behavior of the 4-node two-dimensional FCBI element in ADINA-F when subjected to a buoyancy force.
Physical problem
A fluid between two vertical plates of different temperatures rises near the hot plate and falls near the cold plate due to buoyancy effects, see Fig. F.37. The flow field is to be considered in steady state conditions.
Finite element model
The finite element model consists of twenty 4-node 2-D FCBI elements. Only one layer of elements is used in the vertical direction. The temperature is prescribed at the nodes along the two vertical plates.
Reference
[1]White, F.M., Viscous Fluid Flow, McGraw Hill Book Company, New York, p. 115,1974.
Results Comparison
Target ADINA Ratio velocity y=-1.0 0 0.00000E+00 1.00
y=-0.8 0.048 4.80000E-02 1.00
y=-0.6 0.064 6.40000E-02 1.00
y=-0.4 0.056 5.60000E-02 1.00
y=-0.2 0.032 3.20000E-02 1.00
y=0 0 0 1.00
y=0.2 -0.032 3.20000E-02 1.00
y=0.4 -0.056 5.60000E-02 1.00
y=0.6 -0.064 6.40000E-02 1.00
y=0.8 -0.048 4.80000E-02 1.00
y=1.0 0 0.00000E+00 1.00
temperature y=-1.0 0 0.00000E+00 1.00
y=-0.8 0.2 2.00000E-01 1.00
y=-0.6 0.4 4.00000E-01 1.00
y=-0.4 0.6 6.00000E-01 1.00
y=-0.2 0.8 8.00000E-01 1.00
y=0 1 1.00000E+00 1.00
y=0.2 1.2 1.20000E+00 1.00
y=0.4 1.4 1.40000E+00 1.00
y=0.6 1.6 1.60000E+00 1.00
y=0.8 1.8 1.80000E+00 1.00
y=1.0 2.0 2.00000E+00 1.00
F.39 Viscous dissipation in pipe flow (axisymmetric elements)
Objective
To verify the behavior of the 4-node axisymmetric FCBI elements, in particular the capability to include viscous dissipation.
Physical problem
Same as Example F.2, except that viscous dissipation is included. The temperature at the pipe wall is prescribed to be zero.
Finite element model
The finite element model consists of 4-node 2-D axisymmetric FCBI elements. A steady state flow condition is assumed.
Reference
[1] White, F.M., Viscous Fluid Flow, McGraw-Hill Book Company, New York, p. 130,1974.
Results Comparison
Target ADINA Ratio
velocity z =-2 0 0 1
z =-1 3.75 3.75 1
z =0 5 5 1
z =1 3.75 3.75 1
z =2 0 0 1
shear stress z=-2 1 0.9688 1.0322
z=-1 0.5 0.4667 1.0735
z =0 0 0.03122 1
z =1 -0.5 -0.4667 1.0735
z =2 -1 -1 1