THE AERODYNAMIC OPTIMIZATION DESIGN OF TURBINE CASCADE NONAXISYMMETRIC ENDWALL

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1 Proceedings of Shanghai 2017 Global Power and Propulsion Forum 30 th October 1 st November, GPPS THE AERODYNAMIC OPTIMIZATION DESIGN OF TURBINE CASCADE NONAXISYMMETRIC ENDWALL Hao Liu liuhao@sjtu.edu.cn Liangliang Liu liusoux@163.com Xin Shen shenxin@sjtu.edu.cn Xiaocheng Zhu zhxc@sjtu.edu.cn Hong Yang Shanghai Turbine Works Co.Ltd yanghong@shanghaielectric.com Zhaohui Du zhdu@sjtu.edu.cn ABSTRACT In the present work, an endwall optimization design procedure for reducing secondary flow losses has been developed which allowed complete 3-dimensional parameterization design of the turbine endwall. A so-called shape function and a decay function were used for the definition of the nonaxisymmetric endwall. The shape function was used to control the curvature in the circumferential direction and the decay function was used to control the curvature in the axial direction. The design of the endwall was generated by the product of these two functions. This parametrization allowed influencing the contouring of the specific endwall region. The profile of the endwall has been optimized using automatic numerical optimization by means of an improved efficient global optimization algorithm based on kriging surrogate model. The niching micro genetic algorithm was used to get the correlation vector of Kriging model, which eliminated the dependence of correlation vector starting search points. This method reduced the difficulty of finding appropriate penalty parameters and increased the robustness of the optimization method. The 3D-Reynolds-averaged Navier-Stokes flow solver based on CFX, with a k-ω model for turbulence model, was used for all numerical calculations. An in-house optimization design system was developed to close the loop of the geometry definition, flow solving and the optimization algorithm which allowed the solution of non-linear problems. The numerical simulations demonstrated that the total pressure loss and secondary flow intensity were reduced with the nonaxisymmetric endwall used in the cascade passage. The detailed flow pattern comparisons between the passage with baseline flat endwall and the optimization nonaxisymmetric endwall were given by the numerical simulations method and entropy generation rates analysis were used for the investigation of the secondary flow loss reduction mechanism in the nonaxisymmetric endwall profile cascade. INTRODUCTION The secondary flow losses significantly contribute to the overall losses in turbine cascade, especially with the increasing of the stage loading and airfoil lift for cost and weight reasons. For the past decades, many studies of endwall secondary flows structure have been proposed. Hawthorne[1], Klein[2], Langston[3], Marchal[4], Sharma[5], and Wang[6] provide comprehensive descriptions of the endwall secondary flow model of turbine cascade. A comprehensive review by Sieverding[7] presents the secondary flow studies performed until Later on, Langston[8] reviewed papers related to the secondary flow, including the flow structure investigation either by experiments or by CFD until On the basis of the flow models for the horseshoe vortex, two legs of it, the passage vortex and the cross flow within the passage, researchers tried different methods to minimize the losses associated with these flow structures. The nonaxisymmetric endwall profiling is one of the technology have been verified to achieve a decrease in secondary loss in turbine cascade. Rose[9] designed a nonaxisymmetric hub endwall which redistributed the This work is licensed under a Creative Commons Attribution 4.0 International License CC-BY 4.0 Creative Commons Attribution-NonCommercia 4.0 International License CC-BY-NC 4.0 Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License CC-BY-NC-ND 4.0 PLEASE DELETE THIS TEXT AND THE INAPPROPRIATE LICENCES

2 endwall static pressure to remove the NGV exit circumferential static pressure non-uniformities. For the reason that the endwall static pressure distribution can be controlled by the nonaxisymmetric endwall design, many research works tried to reduce the secondary flow losses by employing the nonaxisymmetric endwall to reduce the endwall cross passage pressure gradient which drives the endwall secondary flow. Harvey[10] et al. and Hartland[11] et al. designed the nonaxisymmetric endwall for a low-speed linear turbine cascade at Durham University and a comprehensive set of measurements were taken in their study. The resulting secondary flows were significantly reduced in the whole passage and the measured net secondary loss was reduced by 30 percent. With the same design method, Gregory Smith[12] redesign the Durham cascade nonaxisymmetric endwall to restricted the profile in the blade passage so that the nonaxisymmetric endwall design was suitable for application to a real machine. The test results indicated that the new profile showed a similar reduction in the strength of the secondary flow but did not produce the same level of loss reduction as the old one designed by Harvey[10] et al. With the refined measurement technique which captured the flow near the endwall more accurately in the cascade, Ingram[13] et al. presented some new results of the Durham cascade with the nonaxisymmetric endwall profile[10-12] to investigate their flow mechanism. In contrast to Gregory Smith, the measurement results shown that the design of Gregory Smith had more reduction in secondary loss because the measurements capture the undesirable corner vortex in the design of Harvey[10] et al. Praisner[14] et al. designed the nonaxisymmetric endwall profiles for three different LP turbine blades. The results showed that the front-loaded blade had a greater reduction in secondary flow losses compare to the after-loaded one with the nonaxisymmetric endwall employed. Sun[15] et al. designed both nonaxisymmetric hub and shroud endwall for an NGV passage. The experimental measurements indicated that a total loss reduction about 11.45% was achieved by comparison to the referenced axisymmetric endwall. The CFD method plays an important role in the nonaxisymmetric endwall optimization design procedure and the design objective selection is also important. Germain[16] highlighted the importance of transitional behavior prediction and indicated that usual CFD codes still have difficulties in predicting secondary losses accurately. Praisner [14]et al. used k-ω model for the turbulence numerical closure and the transition modeling capability described by Praisner and Clark[17] and Praisner[18] et al. was employed for their simulations. The author claimed that although the CFD results did not demonstrate a high level of accuracy compared to the test data, the predicted loss trends between geometries were deemed useful so that the total pressure loss could be chosen as the objective to guide the optimization. Panchal [19] et al. compared the endwall profile designed with minimum SKE values and the one designed with minimum total pressure loss values. The SST k-ω turbulence model was used based on past experience to achieve a higher accuracy of total pressure loss. The author finally suggests that total pressure loss values should be better the optimization objective instead of SKE values. In the present work, the nonaxisymmetric endwall of a large scale linear turbine cascade was optimized to reduce the secondary flow losses. The linear cascade was almost the same with the famous Durham cascade [10-13] except that the blade span was 100mm shorter than Durham cascade design. The nonaxisymmetric endwall profiling for the turbine cascade optimization system consisted of a global optimization algorithm based on kriging surrogate model, nonaxisymmetric endwall profiling parametric method and aerodynamic evaluation numerical approach using 3D Reynolds-Averaged Navier-Stokes. The detailed flow pattern comparisons between the passage with baseline flat endwall and the optimization nonaxisymmetric endwall were given by the numerical simulations method and entropy generation rates analysis were used for the investigation of the secondary flow loss reduction mechanism in the nonaxisymmetric endwall profile cascade. OPTIMIZATION DESIGN SYSTEM The nonaxisymmetric endwall profiling for the turbine cascade optimization system consisted of the global optimization algorithm based on kriging surrogate model, nonaxisymmetric endwall profiling parametric method, and aerodynamic evaluation numerical approach. The flowchart of the presented nonaxisymmetric endwall optimization system was illustrated in Fig. 1. The design objective of the turbine cascade for the optimized nonaxisymmetric endwall profiling was the minimization of total pressure loss coefficient at the cascade exit. The total pressure loss coefficient at the exit was defined as the total pressure difference between inlet and exit divided by the inlet dynamic pressure. Fig. 1 Flowchart of the nonaxisymmetric endwall profiling optimization system for the turbine cascade design Optimization Method In general, evolutionary algorithms are used to ensure reaching the global optimum. However, the high computational costs associated with evaluating a large number of objective functions prevent applications of evolutionary algorithms to practical engineering design problems. In order to cut the prohibitive costs, a low fidelity surrogate model can be used to reduce the number of required objective function evaluations. Queipo[20] et al. and Simpson[21] et al. reviewed various surrogate models used in engineering design. Madsen[22] et al. demonstrated the utility of response surface model in a diffuser design. Marjavaara[23] et al. optimized the shape of a simplified 2

3 hydraulic turbine diffuser using response surface and radial basis neural network based optimization strategy in conjunction with an evolutionary algorithm. In the present work, the endwall has been optimized using an efficient global optimization based on an improved kriging surrogate provided by Wang[24] et al. In their work, a niching micro genetic algorithm was used to get the correlation vector of Kriging model, which eliminated the dependence of correlation vector starting search points. This method reduced the difficulty of finding appropriate penalty parameters and increased the robustness of the optimization method. Nonaxisymmetric Endwall Parameterization Method A so-called shape function and a decay function were used for the definition of the nonaxisymmetric endwall. The shape function was used to control the curvature in the circumferential direction which was prescribed between the cambers of two adjacent blades while the decay function was used to control the curvature in the axial direction. The endwall surface was generated by the product of these two functions. A sinusoidal function was used for the shape function and the decay function decided the amplitude of the shape function in the fixed axial position. B-spline with 8 control points was used for the decay function and the Δr of first and the last point were fixed to zero. Nine parameters were used for the parametrization of the endwall profile. This parametrization method allowed influencing the contouring of the specific endwall region. The turbine liner cascade parametric data and some aerodynamic data sets were illustrated in Table 1. The inlet was one C ax upstream the blade leading edge while the outlet was 4 times C ax downstream the blade tailing edge. The outlet pressure was 1 atm and the periodic boundary condition was added on both sides of the cascade passage. The inlet velocity and turbulence data distribution were acquired from the numerical simulated in a long cube region which has the same height with the cascade region. The data on one slice of the cube region was used to provide the suitable turbulence boundary layer condition to the cascade inlet. Based on this velocity profile, the value of δ was approximately 60 mm and the main flow turbulence was nearly 5%. For the mesh generation, the baseline flat endwall computational grid CGNS file was generated by the ANSYS- ICEM software first, then all the other nonaxisymmetric endwall grids needed in the optimization progress were acquired by rewriting the spanwise direction position of the nodes in this baseline flat endwall CGNS grid file. The nodes movement was as follows, the passage shroud nodes spanwise position were fixed while the nodes blow were moved according to the profile of nonaxisymmetric hub geometric data. The computation grid of a nonaxisymmetric endwall cascade was shown in Fig. 2. Numerical Simulation Method The 3D-Reynolds-Navier-Stokes flow solver based on CFD software ANSYS-CFX 16.0 was used for the cascade aerodynamic evaluation. The cascade Reynolds number in present work was nearly half of the value comparing to a real HP turbine blade, therefore the transition flow effects would have an important influence on the total pressure losses, so a transition SST model was applied to accurately evaluate the effects of the boundary layer transition on the profile and secondary flow losses of the cascade. The transition SST model is based on standard SST k-ω model with a γ-θ transition model added in. The γ - θ transition model brings two additional equations for transition onset criteria and intermittency to predict the laminar-turbulent transition and separated flow transitions Table 1 Cascade design data Inlet Flow Angle o Blade Exit Angle o Blade Chord,C 224mm Blade Axial Chord, C ax 181mm Blade Span 300mm Pitch 191mm Aspect ratio 1.32 Solidity 1.17 Reynolds number(c ax &V ex ) Mach number(inlet/exit) 0.039/0.080 Fig. 2 Computational grid The total pressure loss coefficient of cascade exit was employed to conduct the grid independence and the grid has a limited influence when the grid number is greater than 7.2X10 5. All optimizations were based on this grids, whereas the results were recalculated using the fine grids which had the grids number of 2.3 X10 6 in order to capture the detailed flow mechanism directly. 100 nodes were arranged in the spanwise direction for the fine grids. Both the coarse grid and fine grid were refined on the blade and endwall surface, so the non-dimensional wall distance of y + <1 was satisfied close to walls. Entropy is the best quantity to use when investigating loss in turbomachines[25]. But entropy is a convected 3

4 quantity. This means that the entropy present at any particular location in a machine could have been created at that location or it could have been created upstream and convected into the downstream location. Entropy generation rates in the entropy-transport equation can be used to clearly identify areas of high loss generation because that entropy generation rates only represent the local entropy generation. [26-28] provided the method to add entropy generation rates to the mesh volume of a Reynolds-averaged Navier-Stokes solver with turbulence model. Overall, the cascade downstream aerodynamic performance was improved with the NEW being used. RESULTS AND DISCUSSIONS Optimization Design Results The amplitude Δr of the optimized nonaxisymmetric endwall profile were illustrated in Fig. 3. (a) C pt (b) Yaw Angle Fig. 5 Pitchwise mass flow C pt and yaw angle distributions along the blade span at 128% C ax Fig. 6 illustrated the distribution contours of C pt on the exit plane of 28% axial chord distance downstream the tailing edge. Comparing the results of NEW to BFW, the optimized nonaxisymmetric endwall profiling design had a considerable reduction of the total pressure loss in passage vortex (PV) region. C pt [-] Fig. 4 Amplitude of the endwall In order to be convenient for the following comparison and discusses, the baseline flat endwall was signed by BFW for short, and the nonaxisymmetric endwall was signed by NEW. Both the BFW and NEW case was recalculated by using the fine mesh. At the position of 28% C ax downstream the tailing edge, the mass flow averaged C pt of NEW was comparing to the BFW value of 0.274, a loss reduction of 6.9 percent was achieved according to the fine mesh numerical simulation. The results showed little difference between NEW and BFW mass flow rates due to the little throat area change of the parametric method for the nonaxisymmetric endwall profile. Fig. 5(a) shown the pitch mass flow averaged C pt distribution along the blade span at the location of 28% C ax downstream the trailing edge for both BFW and NEW. The position was normalized by the blade span and only half of the span distribution were illustrated because of the nonaxisymmetric endwall used bottom side only. Comparing to the BFW, the C pt peak value of NEW decreased and the position moved toward to the endwall. Fig. 5(b) shown the pitch wise mass flow averaged yaw angle distribution along the blade span at the location of 28% C ax downstream the trailing edge for both BFW and NEW. With the NEW used, the underturning and overturning were decreased above the 10% spanwise position. Below the position of 10%, the overturning increased to some extent. (a) BFW (b) NEW Fig. 6 Total pressure loss coefficient contours distributions at 128% C ax 4

5 Fig. 7(a,b) illustrated the axial vorticity contours overlapped with the plotted secondary flow vectors on the exit plane 28% C ax downstream the tailing edge. Here the midspan flow direction was defined as the mean flow direction. The secondary velocity vector V sec at any position was obtained by resolving along and normal to the local midspan flow direction at that pitch-wise position. The plotted secondary vectors were obtained by projecting V sec onto the axial viewing plane and the details methods to get plotted velocity were described by Ingram[13] et al. Fig. 7 demonstrated that the passage vortex(pv) and counter vortex(cv) appeared weaker and they both moved close to the endwall when the nonaxisymmetric endwall was used. PV CV suction side leg horseshoe vortex was signed as HV ss and streamlines colored yellow in Fig. 8 (a). The HV ps got into the passage and moved toward to the adjacent blade suction side under the influence of cross-passage pressure gradient. The cross-passage pressure gradient direction also made the HV ps involve more surrounding flows and be enhancement during the development toward downstream. The situation of the HV ss was totally different as shown in Fig. 8 (a), the endwall pressure gradient and endwall cross flow beneath made HV ss lifted off the endwall and quickly dissipated downstream. The streamlines colored black were originated from 1.6% span position of inlet plane. The black streamlines could be used to estimate the scale of the horseshoe vortex. Some cross flow situated more close to the endwall moved along the separation line and rolled up into a vortex as attached the blade suction surface. The vortex was named surface vortex(sv) in the present study and the streamlines were colored blue. In the middle of the passage, the HV ps moving along the endwall encountered the HV ss before reaching the blade surface and the streamlines of HV ss rotated around the HV ps as the axis to the position below the HV ps. After that, the HV ps lifted off the endwall as attaching the blade surface and merged with the SV and then developed into the passage vortex which was signed as PV in Fig. 8 (a). (a) BFW PV CV (a) (BFW) (b) NEW Fig. 7 Axial vorticity contours with plotted Secondary flow vector overlapped distribution at 128% C ax Flow Mechanism The detailed flow pattern acquired from the numerical simulations was used to investigate the flow mechanisms of the optimized nonaxisymmetric endwall profiling on the reduction of the secondary flow loss of turbine cascade. Fig. 8 illustrated the primary secondary flow in the blade passage with endwall surface static pressure contours for both BFW and NEW. For BFW as shown in Fig. 8(a), as the flow approached the blade leading edge, the strong adverse pressure gradients imposed on the approaching flow caused the boundary layer to separate, precipitating the formation of horse vortex. The pressure side leg horseshoe vortex was signed as HV ps and the streamlines colored green while the (b) (NEW) Fig. 8 Secondary flow structure in the passage For NEW as shown in Fig. 8 (b), the pressure side endwall up-concave structure next to the leading edge made the bifurcation position of horseshoe vortex move toward upstream and to the adjacent blade suction side instead of right in front of the blade leading edge comparing to the 5

6 horseshoe vortex bifurcation position of BFW. The HV ps immediately dissipated in the flow downstream because the up-concave structure made little flow precipitating at the stagnation point. This could be confirmed from the black streamlines on the HV ps side. In contrast, more precipitating flow appeared on the HV ss side and a stronger HV ss formed compared to the one of the BFW. In addition, no surface vortex appeared because the pressure gradient in the endwall concave blocked the flow relative to the surface vortex. In the middle of the NEW passage, the flow in the endwall concave rolled up to a weak passage vortex and the HV ss kept between the blade suction surface and passage vortex moving downstream. In summary, with the nonaxisymmetric endwall being used, the pressure side horseshoe vortex was immediately dissipated but a stronger suction side horseshoe vortex appeared and the passage vortex was weaker because both the surface vortex and pressure side horseshoe vortex, which were merged into passage vortex in the BFW passage, were inhibited in the NEW passage. The entropy generation rates were used to investigate the source of loss in the passage, the position with high entropy generation rates meant high loss occurred at that position. The Fig. 9(a),(b) illustrated that the loss caused by the HV ps and passage vortex were dramatically decreased when the NEW was used. The loss caused by the HV ss increased to some extent since the HV ss in the NEW passage was stronger than that in the BFW passage. CONCLUSIONS In this paper, an optimization design procedure for reducing secondary flow losses was performed to design the nonaxisymmetric endwall for a large scale turbine cascade. The optimized design of the nonaxisymmetric endwall had a great reduction of secondary flow loss. The detailed flow pattern comparison in the cascade passage was given by the numerical simulations method and entropy generation rates were used to clearly identify the areas of high loss in the cascade. (1) The CFD method with a transition SST model applied was used to evaluate the aerodynamic performance of the designed turbine cascade. the optimized nonaxisymmetric endwall profiling design achieved a reduction of total pressure loss coefficient C pt about 0.019, which means a total loss reduction about 6.9% by comparison to the baseline flat endwall. The nonaxisymmetric endwall optimization design system was effective at improving the aerodynamic performance by reducing the endwall secondary flow losses. (2) With the nonaxisymmetric endwall being used, the pressure side horseshoe vortex was immediately dissipated but a stronger suction side vortex appeared. For BFW, the pressure side horseshoe vortex merged the surface vortex and turned into passage vortex downstream the passage. The absence of pressure side horseshoe vortex and surface vortex in the NEW passage resulted in a small and wake passage vortex downstream. In addition for NEW, the strong suction side horseshoe vortex almost penetrated the whole cascade passage hindered the passage vortex development to some extent. (3) The entropy generation rates s were used to investigate the loss origin in the cascade passage. The entropy generation rates distribution in the passage with BFW and NEW were compared to figure out the loss reduction mechanism of NEW. Although the stronger suction side vortex brought extra aerodynamic loss to the cascade, the total loss in the cascade still had a reduction result in the suppression of the passage vortex. (a) BFW NOMENCLATURE BFW Baseline flat endwall C Chord C ax Axial chord C pt Total pressure loss coefficient C pt =(p 01 -p 0local )/( p 01 - p s1 ) (b) NEW Fig. 9 Entropy generation rates distribution C ps C SKE H LE Static pressure coefficient C ps =(p s1 -p slocal )/ ( p 01 - p s1 ) Secondary kinetic energy coefficient C SKE = 0.5ρU sec 2 /( p 01 - p s1 ) Blade span Leading edge 6

7 m NGV NEW PS SS SKE TE U U SEC U mid U + V V mid V sec y y + α ρ Mass flow rate Nozzle guide vane Nonaxisymmetric endwall Pressure side Entropy generation rate Suction side Secondary kinetic energy 2 SKE=0.5ρU sec Trailing edge Magnitude of V Magnitude of V sec Magnitude of V mid Dimensionless U Flow velocity vector Midspan flow velocity vector Secondary flow velocity vector Distance from the endwall surface Dimensionless y flow angle density Kinematic viscosity Boundary layer thickness (99%) ω Subscripts Vorticity Wall shear stress 0 Stagnation quantity 1 Passage inlet location ax Axis direction s Static quantity ACKNOWLEDGMENTS This research is supported by the 2011 Aero-Engine collaborative Innovation Plan. REFERENCES [1] Hawthorne, W. R. "Rotational flow through cascades.[j]," Journal of Mechanics and Applied Mathematics, 1955, Vol: 8 (3): [2] Klein, A. "Investigation of the entry boundary layer on the secondary flows in the blading of axial turbines[j]," BHRA T 1004, 1966, Vol. [3] Langston, L., Nice, M., Hooper, R. "Threedimensional flow within a turbine cascade passage[j]," Journal of Engineering for Power, 1977, Vol: 99 (1): [4] Marchal, P. H., and Sieverding, C. H. "Secondary flows within turbomachinery bladings[j]," Proc. Secondary Flows in Turbomachines, AGARD CP, 1977, Vol: 214. [5] Sharma, O. P., Butler, T. L. "Predictions of Endwall Losses and Secondary Flows in Axial Flow Turbine Cascades[J]," Journal of Turbomachinery, 1987, Vol: 109 (2): [6] Wang, H. P., Olson, S. J., Goldstein, R. J., etc. "Flow Visualization in a Linear Turbine Cascade of High-Performance Turbine Blades[J]," Journal of Turbomachinery, 1997, Vol: 119 (1): 1-8. [7] Sieverding, C. H. "Recent Progress in the Understanding of Basic Aspects of Secondary Flows in Turbine Blade Passages[J]," Journal of Engineering for Gas Turbines & Power, 1985, Vol: 107 (2): [8] Langston, L. S. "Secondary Flows in Axial Turbines A Review[J]," Annals of the New York Academy of Sciences, 2001, Vol: 934 (1): [9] Rose, M. G. Non-Axisymmetric Endwall Profiling in the HP NGV s of an Axial Flow Gas Turbine[A]. In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition[C], 1994; V001T01A090. [10] Harvey, N. W., Rose, M. G., Taylor, M. D., etc. "Nonaxisymmetric Turbine End Wall Design: Part I Three-Dimensional Linear Design System[J]," Journal of Turbomachinery, 1999, Vol: 122 (2): [11] Hartland, J. C., Gregory-Smith, D. G., Harvey, N. W., etc. "Nonaxisymmetric Turbine End Wall Design: Part II Experimental Validation[J]," Journal of Turbomachinery, 1999, Vol: 122 (2): [12] Gregory-Smith, D., Ingram, G., Jayaraman, P., etc. "Non-axisymmetric turbine end wall profiling[j]," Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2001, Vol: 215 (6): [13] Ingram, G., Gregory-Smith, D., Rose, M., etc. The effect of end-wall profiling on secondary flow and loss development in a turbine cascade[a]. In ASME Turbo Expo 2002: Power for Land, Sea, and Air[C], 2002; [14] Praisner, T. J., Allen-Bradley, E., Grover, E. A., etc. "Application of Nonaxisymmetric Endwall Contouring to Conventional and High-Lift Turbine Airfoils[J]," Journal of Turbomachinery, 2013, Vol: 135 (6): [15] Sun, H., Li, J., Song, L., etc. Non-Axisymmetric Turbine Endwall Aerodynamic Optimization Design: Part I Turbine Cascade Design and Experimental Validations[A]. In ASME Turbo Expo 2014: Turbine Technical Conference and 7

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