Flow Induced Stresses in a Francis Runner using ANSYS · analysis in a Francis runner was presented...
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Flow Induced Stresses in a Francis Runner using ANSYS José Manuel Franco Nava Instituto de Investigaciones Eléctricas Oscar Dorantes Gómez Instituto de Investigaciones Eléctricas Juan Arturo Roque López Hernández Instituto de Investigaciones Eléctricas Abstract In structural analysis, the finite element method has shown to be a strong numerical technique to provide good engineering accuracy. In the present work, the flow induced stresses in a Francis turbine runner is presented by using the finite element analysis. Loads due to pressure on the blade and centrifugal force based on the rotational speed were considered. Load due to pressure was derived from CFD computations of the runner at different power conditions. In order to increase understanding about combined loads acting on blades, stress distribution over the blades were obtained for three operating conditions at a medium head hydro power plant. Introduction When looking at rehabilitation and maintenance processes to improve the performance of Francis turbine runners, one needs to consider a number of steps. The stress analysis of the runner due to different loading is one of the most important tools that contribute its structural integrity evaluation. In structural analysis, the application of the finite element method has shown to be a strong numerical technique to provide good engineering accuracy. Jacques (1983) presented the application of computation techniques to hydraulic turbine runners to show that CAD/CAM technology can reduce cycle time between initial concept and finished runner. Strain gauge measurements in a operating plant and comparison with finite element analysis in a Francis runner was presented by Bjorndal H. et al, (2001). Mazzouji, F. et al, (2004) work on the application of finite element method to fatigue problems for low head Francis turbines. In the present work, the flow induced stresses in a Francis turbine runner is presented by using the finite element analysis. Loads due to pressure on the blade and centrifugal force based on the rotational speed were considered. Load due to pressure was derived from CFD computations of the runner at different power conditions. In order to increase understanding about combined loads acting on blades, stress distribution over the blades were obtained for three operating conditions at a medium head hydro power plant. This study also aims to establish a reference state of stresses for further comparison after refurbishments of the runner blades. Runner Geometry The runner geometry was generated by a number of 3D sub models, one for each of the main components of the runner, crown, band and a blade. In order to obtain a blade geometry a portable coordinate measurement system based on optical digitalization technology (scanner technology) was used. In this system, the sensor projects a laser stripe across the object to be scanned. The projected stripe is viewed by a camera so that height variations in the object can be seen as changes in the shape of the line. Each viewed stripe forms a profile which is built up from several hundred measured points. The sensor is mounted on an articulated measuring arm which captures an x, y, z position and a vector for each profile, this information enables the profile to be located in 3D space. A number of profiles are captured and positioned in 3D space each second, resulting in a high density 3D point cloud. This 3D point data were processed so as to obtain the blade surfaces. The 3D geometrical models for the crown, band and blades and the final 3D CAD
Transcript of Flow Induced Stresses in a Francis Runner using ANSYS · analysis in a Francis runner was presented...
Flow Induced Stresses in a Francis Runner using ANSYS
José Manuel Franco Nava Instituto de Investigaciones Eléctricas
Oscar Dorantes Gómez Instituto de Investigaciones Eléctricas Juan Arturo Roque López Hernández Instituto de Investigaciones Eléctricas
Abstract
In structural analysis, the finite element method has shown to be a strong numerical technique to provide good engineering accuracy. In the present work, the flow induced stresses in a Francis turbine runner is presented by using the finite element analysis. Loads due to pressure on the blade and centrifugal force based on the rotational speed were considered. Load due to pressure was derived from CFD computations of the runner at different power conditions. In order to increase understanding about combined loads acting on blades, stress distribution over the blades were obtained for three operating conditions at a medium head hydro power plant.
Introduction When looking at rehabilitation and maintenance processes to improve the performance of Francis turbine runners, one needs to consider a number of steps. The stress analysis of the runner due to different loading is one of the most important tools that contribute its structural integrity evaluation. In structural analysis, the application of the finite element method has shown to be a strong numerical technique to provide good engineering accuracy. Jacques (1983) presented the application of computation techniques to hydraulic turbine runners to show that CAD/CAM technology can reduce cycle time between initial concept and finished runner. Strain gauge measurements in a operating plant and comparison with finite element analysis in a Francis runner was presented by Bjorndal H. et al, (2001). Mazzouji, F. et al, (2004) work on the application of finite element method to fatigue problems for low head Francis turbines. In the present work, the flow induced stresses in a Francis turbine runner is presented by using the finite element analysis. Loads due to pressure on the blade and centrifugal force based on the rotational speed were considered. Load due to pressure was derived from CFD computations of the runner at different power conditions. In order to increase understanding about combined loads acting on blades, stress distribution over the blades were obtained for three operating conditions at a medium head hydro power plant. This study also aims to establish a reference state of stresses for further comparison after refurbishments of the runner blades.
Runner Geometry The runner geometry was generated by a number of 3D sub models, one for each of the main components of the runner, crown, band and a blade. In order to obtain a blade geometry a portable coordinate measurement system based on optical digitalization technology (scanner technology) was used. In this system, the sensor projects a laser stripe across the object to be scanned. The projected stripe is viewed by a camera so that height variations in the object can be seen as changes in the shape of the line. Each viewed stripe forms a profile which is built up from several hundred measured points. The sensor is mounted on an articulated measuring arm which captures an x, y, z position and a vector for each profile, this information enables the profile to be located in 3D space. A number of profiles are captured and positioned in 3D space each second, resulting in a high density 3D point cloud. This 3D point data were processed so as to obtain the blade surfaces. The 3D geometrical models for the crown, band and blades and the final 3D CAD
model of the runner are shown in Figure 1- Solid model for the crown, Figure 2- Solid model for the band, Figure 3– Group of runner blades, and Figure 4- Sold model of the runner, respectively.
Figure 1. Solid model for the crown.
Figure 2. Solid model for the band.
Figure 3. Group of runner blades.
Figure 4. Sold model of the runner.
Finite Element Model Because of symmetry, only a section of the domain was used for the finite element analysis. A sector of the runner was obtained by three main geometry sections. The first one was the definition of the blade, which was constructed by staking a number of sections in the span wise direction. The second and third geometry sections were related to the crown and band cross sections.
Once a sector of the runner was defined, a discretized domain was generated. The number of finite elements was defined so as to obtain a three-dimensional element mesh of the blade with a corresponding portion of the band and crown that capture the pressure gradients on the blade surfaces. It is important to mention that during the meshing process, a compromise has to be done in order to evaluate the further solution and time of computations. The sector of the runner was modeled with 5,648 twenty-node solid elements, as shown in Figure 5- Finite element mesh for stress analysis of the blade with corresponding crown and band portions. The full 3D finite element model of the runner is shown in Figure 6- Finite element mesh for stress analysis of the runner.
Figure 5. Finite element mesh for stress analysis of the blade with corresponding crown
and band portions.
Figure 6. Finite element mesh for stress analysis of the runner.
Stress Analysis In this section, loads due to pressure on the blade and centrifugal force based on the rotational speed were considered in order to obtain the stress distribution.
Stresses due to centrifugal force The runner is made of cast stainless steel which has the following material property data:
Mechanical properties Tensile Strength, Yield : Min 550 MPa.
Tensile Strength, Ultimate : Min 755 MPa.
Density: 7695 kg/m3.
Chemical composition
Table 1. Chemical Composition (Wt. %).
C
Min-Max
Mn
Min-Max
Si
Min-Max
Cr
Min-Max
Ni
Min-Max
Mo
Min-Max
P
Min-Max
S
Min-Max
Fe
Min-Max
0.06 1.0 1.0 11.5 -14.0 3.50-4.50 0.40- 1.0 0.04 0.03 82.9-88.1.
Boundary conditions were set in order to obtain the results due to centrifugal force at 12.6 rad/s. Stresses distribution on the pressure and suction sides are shown in Figure 7– Stress results on the pressure and suction sides of a blade. Displacement distribution resulting in the X and Y directions over the full 3D finite element model of the runner is shown in Figure 8- Displacement results in the X direction and Figure 9- Displacement results in the Y direction. It is clear from displacement results that a very good agreement between both directions was achieved.
Figure 7. Stress results on the pressure and suction sides of a blade.
Figure 8. Displacement results in the X direction.
Figure 9. Displacement results in the Y direction.
Stresses due to static pressure In order to obtain the mechanical stresses acting on the blades due to the flow through the runner a computational fluid dynamic analysis (CFD) was carried out. In the CFD analysis, the following considerations were included: the flow rate of the hydraulic turbine change with percentage of turbine power but not linear as shown in Figure 10- Flow rate versus turbine power, only the runner was considered in the control volume with appropriate boundary conditions; at inlet of the domain velocity profiles were given with interpolation of pressure and at outlet an averaged static pressure was imposed. Static pressure distribution on the solid walls of the control volume for the runner was obtained for three different operating conditions (100 %, 85 % and 75 % of turbine power), examples of the CFD results obtained for static pressure is shown in Figure 11- Static pressure distribution on the runner at 100% of load and in Figure 12- Cartesian static pressure plots around the blade at midspan. In Figure 12, the
normalized arc length value of one corresponds to the leading edge of the blade, the value of zero represents the trailing edge. For each of three operating conditions, stress distribution on the pressure and suction sides of the blade are shown in Figure 13- Stress distribution on the pressure and suction sides of the blade at 100% of power, Figure 14- Stress distribution on the pressure and suction sides of the blade at 85 % of power and Figure 15- Stress distribution on the pressure and suction sides of the blade at 75 % of power.
Figure 10. Flow rate versus turbine power.
Figure 11. Static pressure distribution on the runner at 100% of load.
Figure 12. Cartesian static pressure plots around the blade at midspan.
Figure 13. Stress distribution on the pressure and suction sides of the blade at 100% of power.
Figure 14. Stress distribution on the pressure and suction sides of the blade at 85 % of power.
Figure 15. Stress distribution on the pressure and suction sides of the blade at 75 % of
power.
Stresses due to static pressure and centrifugal force Loads due to static pressure on the blade and centrifugal force based on the rotational speed were considered. In order to obtain the combined stress solution, static pressure distribution the blade that was obtained for three different operating conditions (100%, 85% and 75% of turbine power) was included within a multi analysis session. Figure 16- Stress distribution due to combined loads on the pressure and suction sides of the blade at 100% of power, Figure 17- Stress distribution due to combined loads on the pressure and suction sides of the blade at 85 % of power and Figure 18- Stress distribution due to combined loads on the pressure and suction sides of the blade at 75 % of power, respectively. Displacement distribution resulting in the X and Y directions over the full 3D finite element model of the runner is shown in Figure 19- Displacement results in the X direction under combined loads and Figure 20- Displacement results in the Y direction under combined loads. It is clear from displacement results that a very good agreement between both directions was achieved.
Figure 16. Stress distribution due to combined loads on the pressure and suction sides of the blade at 100% of power.
Figure 17. Stress distribution due to combined loads on the pressure and suction sides of
the blade at 85 % of power.
Figure 18. Stress distribution due to combined loads on the pressure and suction sides of
the blade at 75 % of power.
Figure 19. Displacement results in the X direction under combined loads at 100% of power.
Figure 20. Displacement results in the Y direction under combined loads at 100% of power.
Analysis Results & Discussion From the results it can be seen that stresses due to centrifugal force do not contribute significantly to the combined stress distribution. The maximum stresses for each case of loading are presented in Table 2.
Table 2. Maximum stresses.
Description (MPa)
Maximum stress due to centrifugal force 38.1
Maximum stress due to static pressure at 100 % of power 78.4
Maximum stress due to static pressure at 85 % of power 80.5
Maximum stress due to static pressure at 75 % of power 73.2
Maximum stress due to combined loads at 100 % of power 115
Maximum stress due to combined loads at 85 % of power 118
Maximum stress due to combined loads at 75 % of power 111
Conclusion The maximum stresses at all cases of loading conditions are 1/5 below the yield strength. From the results it can be seen that stresses due to centrifugal force do not contribute significantly to the combined stress distribution. The analysis presented in this paper represents an initial characterization of the structural evaluation of the runner of a medium head hydroelectric power station. The number of finite elements included in the FEM model was able to capture the pressure gradients on the blade surfaces obtained from the CFD results.
Acknowledgements The authors wish to acknowledge the support of the Comisión Federal de Electricidad (CFE), and particularly to Engineer José Manuel Fernández Dávila and his group.
References Bjorndal H., Moltubakk, T. and Aunemo, H., (2001), Flow induced stresses in a medium Francis runner, Proceedings of the 10th International Meeting of the Working Group on The Behaviour of Hydraulic Machinery Under Steady Oscillatory Conditions, Norway.
Jacques Y. McNabb, (1983), The application of CAD/CAM technology to hydraulic turbine runners, V.45, Proceedings of the American Power Conference, pp1085-1090.
Mazzouji, F., Francois, M., Tomas, L., Paquet, M., Coustom, M. and Vuillerod, G., (2004), Refinements in Francis turbine design, Hydropower & Dams, Issue One, pp53-58.
