3 CFD for industrial turbomachinery designs
3.10 CFD Applications in Turbomachine Design
3.10.1 Flow solver for section analysis
A time-marching algorithm was used in the present cascade flow computations [2,20,22,23,29]. The computation starts with a rough perturbation, which develops under certain boundary conditions. In this approach, the governing equations are replaced by a time-difference approximation with which steady or time-dependent flows of interest can be solved at each time level. The details of the governing equa-tions and the method of solving the equaequa-tions are discussed in previous secequa-tions.
The discussion has been extended for many years for the optimum type of the mesh that should be used for turbine or compressor blade flow calculation [15,16].
The more orthogonal the grid, the smaller will be the numerical errors due to the discretization. However, no one type of grid is ideal for blade-to-blade flow calculation. In this study, the H-type mesh is used. Another problem for the blade-to-blade mesh is the trailing edge mesh and the trailing edge Kutta condition [7].
The authors have noticed that the number of mesh points near the trailing edge points strongly influence the loss calculation. Here, a realistic method is proposed;
that is, when the mesh on the trailing edge circle is more than 10 points, an explicit viscous Kutta condition [17] is applied on the training edge circle which allows flow leaving the blade smoothly.
The mesh refinement study was conducted prior to the calculations [2,3]. It is shown that the mesh size of 110× 45 with 80 points on the blade surface in the blade-to-blade section is sufficient. The H-mesh [2,3] was used in all the computations.
The computational mesh is shown in Figure 3.58. A typical convergence history of the calculation is shown in Figure 3.59. It is demonstrated that the present code has a good convergence. In this study, this code was used in the two-dimensional airfoil section analysis and optimization.
3.10.2 Optimization
Turbine and compressor designs faced the challenge of high efficiency and reliable blade design. Design techniques are typically based on the engineering experience and may involve much trial and error before an accepted design is found. The ability of the three-dimensional codes and the ability to perform a three-dimensional flow calculation are difficult to improve the design. The three-dimensional approach is a way to help designers do some parameter study and compare the numerical
Figure 3.58. Computational mesh.
Number of steps
Error x 1000
0 500 1000 1500 2000
100
10−1
10−2
10−3
Figure 3.59. Typical convergence history.
study with testing in order to improve the design. The three-dimensional method is used for parameter studies, like lean, bow, and sweep effects. The two-dimensional analysis developed in the study is used to optimize blade section airfoil.
The blade design often starts with two-dimensional airfoil section. Some of the design parameters are obtained by through-flow optimization and vibration and heat transfer analysis, for example, the solidity and number of blades. And most of the parameters are optimized through the sectional design. For example, leading-and trailing-edge radii, stagger angle, leading-and maximal thickness position. The final three-dimensional analyses are used to make lean, bowed, and sweep modification of the blades.
The optimization process used in this study was based on the constrained opti-mization method [26]. If the objective function to be minimized is F(X) and constraint functions is gj(X), the optimization problem can be formulated by the
objective and constraint functions as:
∇F(X) +
λj∇gj(X)= 0 (78)
where λj are the Lagrange multipliers and X is the vector of the objective. The finite differencing method can be used to obtain the gradients of objective and con-straint functions with respect to design variables and concon-straints. Many commercial optimization packages are available as an optimizer to design problems [26].
The objective function of this study is adiabatic efficiency. The optimization objective is to obtain the highest efficiency under given constraints. Foe more convenience, the total pressure loss is used as an objective variable to judge the design. The definition of the total pressure loss in this study is:
ξ= (p∗in− p∗out)
H (79)
where H is the outlet dynamic head of the exit plane.
Two-dimensional section optimization
In this study, a compressor stator blade originally stacked up by using NACA 65 was redesigned and optimized. In this design, the thickness of the airfoil, chord, stagger angle, and inlet and outlet flow parameters were fixed. The designed blade was used to replace the old blade. The section design optimization was mainly achieved through adjusting the section maximum thickness location. It was found that the maximum thickness locations influence the losses and performance. In this study, five sections were selected as design section. All section designs used the similar method and procedure. As an example, the results presented here are the design information for 50% span section.
Figures 3.60 through 62 show the Mach number distributions of the design blades with different maximum thickness locations. Figure 3.63 shows the relation-ship between total pressure losses and location of the maximum thickness. It was shown that the Mach number distributions changed with the maximum thickness.
The change in the Mach number distributions will influence the boundary-layer development and influence the losses of the section. It was found that there is an opti-mum location of the maxiopti-mum thickness. Studies have also shown that this location changes with flow conditions and stagger of the airfoil. After optimization study, the airfoil section with highest efficiency was selected. The airfoil was stacked up using a smooth leading edge curve method. Before the airfoil was selected as the final blade, the three-dimensional analysis was performed to investigate the benefits of the three-dimensional blade features. Three-dimensional analysis showed that after section optimization the airfoil performance was improved, as shown in Figure 3.64.
However, the end wall region did not show significant improvement. Some three-dimensional features were used to reduce the losses and increase the efficiency.
Three-dimensional blading
Three-dimensional CFD analysis codes were used to guide the three-dimensional final modification of the two-dimensional section stackup. Some parameters were
0.65
0.75
0.75 0.30.65 0.15 0.05
0.35 0.65
0.85 0.45
0.35 0.55
0.05 0.55 0.25
0.55
0.55
0.45
Figure 3.60. Mach number distributions for maximum thickness at 15% chord.
0.550.65 0.35
0.55 0.65 0.45
0.75
0.25 0.35
0.65
0.45 0.15 0.25 0.05 0.55
0.25 0.05
0.350.65 0.550.15
0.25 0.45
Figure 3.61. Mach number distributions at maximum thickness at 25% chord.
Figure 3.62. Mach number distributions at maximum thickness at 45% chord.
0.35 0.4 0.45 0.5 0.55
15 25 35 45
Maximum thickness position (%)
Total pressure loss (%)
Figure 3.63. Total pressure losses Vs maximum thickness location.
selected to do the study based on design experience. In this redesign, the three-dimensional feature-bowed blade was used to reduce the secondary losses. In the three-dimensional blading, the optimizer will not be used in this study, because optimization with optimizer like the three-dimensional code is very time consuming. Although the mesh sizes, turbulence models and mixing between the blade rows strongly influence the optimization results, the process propose here provide a way to drive a better design. In the current study, three-dimensional optimization was obtained through parameter study.
0 10 20 30 40 50 60 70 80 90 100
0 3 6 9 12 15
Total pressure loss (%)
Radial height (%)
After optimization After redesign sections NACA 65 sections
Figure 3.64. Total pressure losses along with blade span.
(a) (b) (c)
Figure 3.65. Static pressure distribution on the suction surface. (a) Original NACA section blade. (b) Before 3D optimization. (c) After 3D optimization.
In this study, only bow feature is applied. The bow location and degree of the bow were selected as study parameters. It was found that the 15 degree bow located at 30% of the span can eliminate separation and get better performance. The three-dimensional analysis showed that after two-three-dimensional section optimized design, the flow in most of the spanwise locations remained attached and well behaved although it had a small region of end wall separation on the section side, as shown in Figures 3.65 through 68. After the bow was introduced the flow around the airfoil on both tip and root end wall was attached. The total pressure losses were reduced, as shown in Figure 3.64. This study showed that the total section efficiency increased by about 3% as compared with the original blade. Both two-dimensional
(a) (b) (c)
Figure 3.66. Axial velocity contour near blade suction surface. (a) Original NACA section blade. (b) Before 3D optimization. (c) After 3D optimization.
(a) (b)
Figure 3.67. Velocity vector near the root section near the trailing edge suction surface. (a) Before 3D optimization. (b) After 3D optimization.
section design and three-dimensional optimization increased the efficiency with similar percentage. It has been shown that both two-dimensional optimization and three-dimensional study are important. However, three-dimensional blading depends more on the experience of the designer.
It is important to point out that, based on the design experience, the three-dimensional analysis results normally are not accepted as final shape. The selection of the final configuration was accepted through small adjustments based on expe-rience to obtain high performance and stability. After three-dimensional analysis, some small adjustments were made based on the possible manufacturing uncertain-ties and applications. For example, the compressor stator design in this study was recambered to increase exit angle by about 1.5 degrees to increase the compressor surge margin.
(a) (b)
Figure 3.68. Velocity vector near the tip section near the trailing edge suction surface. (a) Before 3D optimization. (b) After 3D optimization.
The flow field around turbine and compressor blades exhibits very complex flow features. The flow field involves various types of loss phenomena, and hence high-level flow physics is required to produce reliable flow predications. The blade design process is a very time consuming process and the optimization process is very complicated. The method developed in this study for the airfoil section and blade design and optimization is one successful process and very easy for adapting in the aerodynamic design. In this study, a two-dimensional code was used for section design instead of three-dimensional code, which provides an economic way for design and optimization. The three-dimensional blades were optimized after stacking up the two-dimensional sections. The lean, bowed, and swept features of the three-dimensional blade were created during three-dimensional optimization.
It was shown that both two- and three-dimensional design and analysis were the backbones of the blade aerodynamic designs. The results show that both the airfoil shape optimization and the three-dimensional optimization can be used to improve the performance of compressor and turbine blade.
References
[1] Xu, C., and Amano, R. S. On the Development of Turbine Blade Aerodynamic Design System, ASME and IGTI Turbo Expo, 2001-GT-0443. New Orleans, LA, USA, June 4–7, 2001.
[2] Xu, C., and Amano, R. S. A Hybrid Numerical Procedure for Cascade Flow Analysis, Numer. Heat Transfer, Part B, 37(2), pp. 141–164, 2000.
[3] Xu, C., and Amano, R. S. An Implicit Scheme for Cascade Flow and Heat Transfer Analysis, ASME J. Turbomach., 122, pp. 294–300, 2000.
[4] Japikse, D. Centrifugal Compressor Design and Performance, Concepts ETI, Inc., Wilder VT, USA, 1996.
[5] Wellborn, S. R., and Delaney, R. A. Redesign of a 12-Stage Axial-Flow Compressor Using Multistage CFD, 2001-GT-345, ASME and IGTI Turbo Expo, New Orleans, LA, USA, June 4–7, 2001.
[6] Lakshminarayana, B. An Assessment of Computational Fluid Dynamics Techniques in the Analysis and Design of Turbomachinery—the 1990 Freeman Scholar Lecture, ASME J. Fluids Eng., 113, pp. 315–352, 1991.
[7] Xu, C. Kutta Condition for Sharp Edge Flows, Mech. Res. Commun., 25(4), pp.
425–420, 1998.
[8] Xu, C. Surface Vorticity Modeling of Flow Around Airfoils, Comput. Mech., 22(6), pp. 1998.
[9] Xu, C., and Yeung, W. W. H. Discrete Vortex Method for Airfoil with Unsteady Separated Flow, J. Aircraft, 33(6), pp. 1208–1210, 1996.
[10] Xu, C., Yeung, W. W. H., and Gou, R.W. Inviscid and Viscous Simulations of Spoiler Performance, Aeronaut. J., 102(1017), pp. 399–405, 1998.
[11] Xu, C., and Yeung, W. W. H. Unsteady Aerodynamic Characteristics of Airfoil with Moving Spoilers, J. Aircraft, 36(3), pp. 530–538, 1999.
[12] Xu, C., and Yeung, W. W. H. Numerical Study of Unsteady Flow Around Airfoil with Spoiler, 65(1), 164–171, 1998.
[13] Michos, A., Bergeles, G., and Athanassiadis, N. Aerodynamic Characteristics of NACA0012 Airfoil in Relation to Wind Generators, Wind Eng., 7, pp. 1–8, 1985.
[14] Singh, G., Walker, P. J., and Haller, B. R. Development of 3D Stage Viscous Time-Marching Method for Optimisation of Short Stage Heights, Proceedings of the European Conference on Turbomachinery, Erlangen, 1995.
[15] Turkel, E., and Vatsa, V. N. Effect of Artificial Viscosity on Three-Dimensional Flow Solutions, AIAA J., 32(1), pp. 39–45, 1994.
[16] Lin, H., Yang, D. Y., and Chieng, C. C. Variants of Biconjugate-Gradient Method for Compressible Navier–Stokes Solver, AIAA J., 33(7), pp. 1177–1184, 1995.
[17] Weingold, H. D., Neubert, R. J., Behlke, R. F., and Potter, G. E. Bowed Stators: An Example of CFD Applied to Improve Multistage Compressor Efficiency, J. Turbomach., 119, 1997.
[18] Sasaki, T., and Breugelmans, F. Comparison of Sweep and Dihedral Effects on Compressor Cascade Performance, ASME Paper No. 97-GT-2, 1997.
[19] Kawagishi, H., and Kawasaki, S. The Effect of Nozzle Lean on Turbine Efficiency, Proceedings of ASME International Conference on Joint Power Generation, October, 1991.
[20] Wallis, A. M., and Denton, J. D. Comparison of design intent and experimental measurements in a low aspect ratio axial flow turbine with three-dimensional blad-ing. Proceedings, ASME International Gas Turbine and Aeroengine Congress and Exhibition, Stockholm, Sweden, ASME Paper 98-GT-516 (June 1998).
[21] Gonzalez, J., Fernandez, J., Blanco, E., and Santolaria, C. Numerical Simulation of Dynamic Effects due to Impeller-Volute Interaction in a Centrifugal Pump, ASME J.
Fluids Eng., 124, pp. 348–355, 2002.
[22] Chima, R. V. Explicit Multigrid Algorithm for Quasi-Three-Dimensional Viscous Flows in Turbomachnery, J. Propul. Power, 3(5), pp. 397–405, 1987.
[23] Inoue, M., and Furukawa, M. Artificial Dissipative and Upwind Schemes for Tur-bomachinery Blade Flow Calculations, Numerical Methods for Flow Calculation in Turbomachines, Von Karman Institute for Fluid Dynamics Lecture Series, 1994-06, 1994.
[24] Li, H., Chen, S., and Martin, H. F. Two Dimensional Viscous Blade Flow Code Using Shifted Periodic Grids, ASME Paper No. 97-GT-516, 1997.
[25] Vanderplaats, G. N. Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York, 1984.
[26] Chung, J., Shim, J., and Lee, K. D. Shape Optimization of High-Speed Axial Com-pressor Blades Using 3D Navier–Stokes Flow Physics, ASME and IGTI Turbo Expo, 2001-GT-0594, New Orleans, LA, USA, 2001.
[27] Dunham, J. Analysis of High Speed Multistage Compressor Throughflow Using Spanwise Mixing, ASME Paper No. 92-GT-13, 1992.
[28] Farin, G. Curves and Surfaces for Computer Aided Geometrical Design: A Practical Guide, 3rd Edition, Academic Press, Inc., San Diego, 1993.
[29] Arnone, A., and Swanson, R. C. A Navier–Stokes Solver for Turbomachinery Applications, ASME J. Turbomach., 115(2), pp. 1556–1563, 1993.
[30] Chima, R. V. Explicit Multigrid Algorithm for Quasi-Three-Dimensional Viscous Flows in Turbomachnery, J. Propul. Power, 3(5), pp. 397–405, 1987.
[31] Chakravarthy, S. R., Anderson, D. A., and Salas, M. D. The Split Coefficient Matrix Method for Hyperbolic Systems of Gasdynamics Equations, AIAA Paper No. 80-0268, 1980.
[32] Baldwin, B. S., and Lomax, H. Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows, AIAA Paper 78-257, 1978.
[33] Amineni, N. K., and Engeda, A. Pressure Recovery in Low Solidity Vaned Diffusers for Centrifugal Compressors, 97-GT-472, 1997.
[34] Hylton, L. D., Mihelc, M. S., Turner, E. R., Nealy, D. A., and York, R. E. Analytical and Experimental Evaluation of the Heat Transfer Distribution Over the Surfaces of Turbine Vanes, NACA CR-168015 DDA EDR 11209, 1983.
[35] Kwon, O. K. Navier–Stokes Solution for Steady Two-Dimensional Transonic Cascade Flows, ASME J. Turbomach., 110(2), pp. 339–346, 1988.
[36] Younis, M. E., and Camarero, R. Finite Volume Method for Blade to Blade Flow Using a Body Fitted Mesh, AIAA J., 19(11), pp. 1500–1502, 1981.
[37] Denton, J. D. An Improved Time-Marching Method for Turbomachinery Flow Calculation, ASME J. Eng. Gas Turbines Power, 105, pp. 514–521, 1983.
[38] Sieverding, C. H., ed. Description of Test Cases and Presentation of Experimental Results, Von Karman Institute for Fluid Dynamics Lecture Series, 1982-05, Rhode-Saint-Genese, Belgium, 1982.
[39] Xu, C., and Amano, R. S. Computational Analysis of Pitch-Width Effects on the Secondary Flows of Turbine Blades, Comput. Mech., 34(2), pp. 111–120, 2004.
[40] Perdichizzi, A., and Dossena, V. Incidence Angle and Pitch-Chord Effects on Secondary Flows Downstream of a Turbine Cascade, ASME J. Turbomach., 115, pp. 383–391, 1993.
[41] Hodson, H. P., and Dominy, R. G. Three-Dimensional Flow in a Low-Pressure Turbine Cascade at Its Design Condition, ASME J. Turbomach., 109, pp. 177–185, 1987.
[42] Gregory-Smith, D. G., and Clerk, J. G. E. Secondary Flow Measurement in a Turbine Cascade with High Inlet Turbulence, ASME Paper No. 90-GT-20, 1990.
[43] Kiss, T., Schetz, J.A., and Moses, H. L. Experimental and Numerical Study of Transonic Turbine Cascade Flow, AIAA J., 34, pp. 104–109, 1996.
[44] Langston, L. S., Nice, M. L., and Hooper, R. M. Three-Dimensional Flow within a Turbine Cascade Passage, ASME J. Eng. Power, 99, pp. 21–28, 1977.
[45] Senoo, Y., Hayami, H., and Ueki, H. “Low-solidity tandem . . .” 1983, ASME Paper No. 83-GT-3. ASME Gas Turbine Conference, Phoenix, Arizona, USA.
[46] Kenny, D. P. The History and Future of the Centrifugal Compressor in Aviation Gas Turbine, 1st Cliff Garrett Turbomachinery Award Lecture, Society of Automotive Engineers, SAE/SP-804/602, 1984.
[47] Weber, C. R., and Koronowski, M. E. Meanline Performance Prediction of Volutes in Centrifugal Compressors, ASME 31st Gas Turbine Conference and Exhibit, Dusseldorf, Germany, 86-GT-216, 1987.
[48] Dong, R., Chu, S., and Katz, J. Effect of Modification to Tongue and Impeller Geometry on Unsteady Flow, Pressure Fluctuations and Noise in a Centrifugal Pump, ASME J.
Turbomach., 119, pp. 506–515, 1997.
[49] Arora, J. S. Introduction to Optimum Design, McGraw-Hill, NY, USA, 1998.
[50] Duccio Bonaiuti, Andrea Arnone, Mirco Ermini, Analysis and Optimization of Tran-sonic Centrifugal Compressor Impellers Using the Design of Experiments Technique, gt-2002-30619, 2002, Amsterdam, The Netherlands.
[51] Harry, M. J. The Nature of Six Sigma Quality, Motorola University Press, Shaumburg, IL, USA, 1997.
[52] Ayder, E. Experimental and Numerical Analysis of the Flow in Centrifugal Compressor and Pump Scrolls, Ph.D. dissertation, Von Karman Institute, 1993.
[53] Ayder, E., and van den Braembussche, R. Numerical Analysis of the Three-Dimensional Swirling Flow in Centrifugal Compressor Scrolls, ASME J. Turbomach., 116, pp. 462–468, 1994.
[54] Ayder, E., van den Braembussche, R., and Brasz, J. J. Experimental and Theoretical Analysis of the Flow in a Centrifugal Compressor Scroll, ASME J. Turbomach., 115, pp. 582–589, 1993.
[55] Gu, F., Engeda, A., Cave, M., and Liberti, J. A Numerical Investigation on the Scroll/Diffuser Interaction due to the Axial Distortion at the Impeller Exit, ASME J. Fluid Eng., 123, pp. 475–483, 2001.
[56] Sideris, M. Circumferential Distortion of the Flow in Centrifugal Compressors due to Outlet Scrolls, Ph.D. dissertation, Von Karman Institute, 1998.
[57] Gonzalez, J., Fernandez, J., Blanco, E., and Santolaria, C. Numerical Simulation of Dynamic Effects due to Impeller-Volute Interaction in a Centrifugal Pump, ASME J.
Fluids Eng., 124, pp. 348–355, 2002.
[58] Xu, C., and Amano, R. S. Eliminating Static Pressure Distortion by a Large Cut Back Tongue Volute, Barcelona, Spain.
[59] Chu, S., Dong, R., and Katz, J. Relationship between Unsteady Flow, Pressure Fluctua-tions, and Noise in a Centrifugal Pump—Part B: Effects of Blade-Tongue InteracFluctua-tions, ASME J. Fluids Eng., 117, pp. 30–35, 1995.
[60] Irabu, K., Tamazato, E., and Teruya, I. Velocity Measurement of Flow around a Scroll Tongue of the Vaneless Radial Diffuser, Proceedings of 3rd Asia Symposium on Visualization, Japan, 1994.
[61] Hah, C., and Wennerstrom, A. J. Three-Dimensional Flowfields Inside a Transonic Compressor with Swept Blades, 90-GT-359, Brussels, Belgium 62. computational Fluid Dynamics Symposium on Aeropropulsion, NACA CP-10045, Apr. Cleveland, Ohio, 1990
[62] Kunz, R. F., and Lakshminarayana, B. Computation of Supersonic and Low Subsonic Cascade Flows Using an Explicit Navier-Stokes Technique and the k-ε Turbulence Model, ANSA CP-10045, 1990.
[63] Basi, F., Rebay, S., and Savini, M. “A Navier- ...”, AGARD-CP-527, “Heat Transfer and Cooling in Gas Turbines” Oct. 1992, pp. 41.1 to 41.16.