Design and CFD Analysis of a Curtis Turbine Stage

Transcription

1 PROCEEDINGS OF ECOS THE 9 TH INTERNATIONAL CONFERENCEON EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS JUNE 19-3, 016, PORTOROŽ, SLOVENIA Abstract Design and CFD Analysis of a Curtis Turbine Stage Manuele Achille, Simone Cardarelli, Fabio Pantano, Massimiliano Zito a a Department of Mechanical and Aerospace Engineering, University Roma Sapienza, Roma, Italy, massi.zito1991@gmail.com The preliminary design and CFD analysis of a high pressure Curtis wheel, used as a first stage in a steam turbine, are described. Starting from a thermodynamic evaluation of the process, the steam flow in the combined stage (rotor, intermediate stator row, second rotor) has been examined. At first a two-dimensional geometry, then a three-dimensional model of the two rotor blade rings has been implemented using a CAD software (SOLIDWORKS ), then simulated using a commercial CFD package (ANSYS-FLUENT ). The first guess blade profiles chosen during the initial design have then been corrected on the basis of the CFD feedback throughout several simulations in a modify-and-test procedure, in order to achieve a better stage efficiency. In particular, the aim of this paper is to explore how first attempt blade design based on velocity triangles can be improved, with the commercial CFD software ANSYS FLUENT. Keywords: Steam Turbine, Impulse, Curtis, CFD, high-pressure 1. Introduction While Curtis wheel technology is widely known since about a century, its presence in turbine engineering is still strong, especially in electric power production, thanks to some properties like compact dimensions for a given power with respect to other stage designs and the possibility of power regulation through nozzle governing. Due to this last aspect, Curtis wheel is still nowadays necessary and widely used as first stage of steam turbines. In velocity compound turbines, the steam, usually at high pressure, is expanded by nozzles, losing static pressure with a strong velocity gain; this gain can be critical, since it is often close to local sonic conditions. The high velocity steam then enters the first rotor blade set, exchanging energy with it and leaving it in a direction not directly usable in next row; hence, a stator blades row must be used, with the only function of redirecting the flow to optimal angle for the second and last rotor blade set. Note that both rotor blade sets are positioned on the same wheel. Leaving the Curtis stage, the steam has lost a remarkable quantity of enthalpy, and can be expanded in the following lower pressure, higher efficiency reaction stages. Since the number of blade rows for this technology has been, through years, fixed to no more than three, but most commonly two, in this particular case it has been decided to use two rows, since using three rows would not yield much more power while it would instead lower the stage efficiency which, by Curtis turbine nature, is not as high as those of low pressure reaction stages. This paper, starting from common industrial operational conditions, and because of a lack in literature of papers focused on the CFD design of impulse turbines, focuses on the design of Curtis stage wheel, with particular support from CFD in correcting blade profiles in order to better follow the steam behavior through the whole stage. 1

2 . Stage Design Initial steam conditions (before entering nozzles) used in this project are: Table 1. Initial steam conditions. Parameter T 0 p 0 Value 550 C 170 bar while other operating conditions are: Table. Operating conditions. Parameter m n Δh Value 15 kg s 3000 rpm 00 kj kg As first design step, steam tables have been used, in order to completely define steam parameters before nozzle expansion. Table 3. Parameters before and after nozzle expansion. Parameter T 1 ρ 0 h 0 p 1 ρ 1 h 1 v s1 Value 440 C kg m kj kg 90 bar kg m kj kg 615 m s Nozzle expansion yields v 1 = Δh = 63 m s which is greater than local sound velocity v s 1. This would lead to a convergent-divergent De Laval nozzle that may cause problems during power regulation (for more information see ref [6]). For this reason it s been decided to use a slightly lesser Δh so that the actual post-nozzle velocity coincides with the local sound velocity. This means using: Δh actual = 189 KJ Kg. Since for impulse turbines R ρ = 0, and being for the first row:

3 and for the second row: R ρ = h 1 h h tot tot 0 h = L eu L eu V 1 V = 1 V 1t + V t U (1) R ρ = 1 V 3t + V 4t U to have maximum work it s imposed V 4t = 0, and neglecting deviator losses V 3t = V t, this leads to the condition of maximum efficiency: hence Δψ =, for each row. ψ So we obtain { 1 = 4 ψ = ψ 3 = () V 3t = V t = U (3) V 1t = 4U (4) As for Curtis turbines constructive practices [15] the angle α 1 = 18 has been chosen, φ can be defined: This way both U and V 1m are known: φ 1 = ψ 1 tanα 1 = 1.3 V 1m = 190 m s U = 146 m/s It s so possible to define the medium diameter of the row: D = U ω = 0.93m The velocity triangles for the first stage row, considering that for impulse turbine blades β 1 = β, are shown in figures 1 and, with the corresponding values (Tab.4-7). Note that in drawing these velocity diagrams it s assumed as hypothesis that the flow leaves the trailing edge at the edge s angle in the coordinate frame attached to the blade. As a first approximation, no viscous effects are considered. Table 4. Velocity triangle values (first row, inlet) α 1 β 1 V 1t V 1m W 1t W 1m m s 190 m s 438 m s 190 m s Table 5. Velocity triangle values (first row, outlet) α β V t V m W t W m m s 190 m s 438 m s 190 m s Fig. 1. Velocity triangles for first rotor row. 3

4 The stator intermediate blades mirror V with respect to the meridian direction, thus offering to the second rotor row V 3. Table 6. Velocity triangle values (second row, inlet) α 3 β 3 V 3t V 3m W 3t W 3m m s 190 m s 146 m s 190 m s Table 7. Velocity triangle values (second row, outlet) α 4 β 4 V 4t V 4m W 4t W 4m m s 190 m s 146 m s 190 m s Fig..Velocity triangle for second rotor row..1 Performance For the first rotor set, we have: L I = (V 1 V ) + (U 1 U ) + (W W 1 ) But being for axial turbines U 1 = U and for impulse turbines W 1 = W : Also: And so: The resulting turbine efficiency is: L I = V 1 V L II = V 3 V 4 = V 1t V t 18 KJ Kg = V 3t 4 4 KJ Kg L Curtis = L I + L II = V 1 V 4 KJ 170 Kg η turbine = L Curtis Δh actual = 0.9 (5)

5 In order to take into account losses due to: ventilation, viscous friction, and other mechanical losses, we consider an organic efficiency equal to 0.85 [1]: η Curtis = η turbine η org = 0.76 which is consistent with modern Curtis turbine efficiency[13]. Moreover it is possible to evaluate the characteristic velocity coefficient as recommended in ref [1]: And the specific diameter [1]: n s1 = k ( U ) ( V 0.5 1m ) = 0.5 V 1 V 1 d s = DΔh1 4 Q = 7.41 This leads to an expected [16] η Balje = 0.8 which is consistent with the obtained result. The power to the shaft can be then evaluated as: P shaft = m L Curtis η org 31 MW The minimum shaft diameter is evaluated according to [1]: 3 D shaft = S 5.09 P shaft 0.65 m ωτ max being τ max = 30 MPa and the safety coefficient S =.5. Note that this would be the shaft diameter for the Curtis turbine on its own, so for multi stage application this diameter has no validity, since total power would be much greater.. Blade design The height of the blades is defined by considering the volumetric flow rate. Being: withδ b =0.85 [1], we obtain: Q = πd3 8 (1 χ )φ 1 ωδ b (6) χ = 0.95 which means external diameter approximately D e = 0.95 m and internal diameter D i = 0.91 m, consequently the blades height h = cm. In similarity with common Curtis turbines [13], blade aspect ratio has been set to 1, meaning that the value of blade chord is l = cm. For the same similarity principle the pitch has been set to t = 1 cmand blade maximum thickness s = 0.5 cm. The number of blades was then chosen to respect the volumetric flow rate: z = Q htv 1m δ b 15 1 Note that in this case it s not possible using the standard n s computational formula. 5

6 In order to reduce viscous losses due to interaction between evolving flow and turbine casing wall, rings should be jointed at the tip of the blades; as an extra result, this provides a greater robustness to rotor rows. Blade models have been created using Solidworks software, by using geometric relations directly from velocity triangles. This led to first attempt blade shape which was later simulated in CFD analysis and then modified to achieve better flow dynamics...1 Preliminary blade sizing First rotor blade set profile: Second rotor blade set profile Fig. 4. First row blade profile. Fig. 3. First row blade model. Fig. 5. Second row blade profile. 3. Computational Fluid Dynamics CFD simulation Fig. 6. Second row blade model. For turbine computational analysis, software ANSYS FLUENT 15.7 has been used. The simulation setup and execution is composed of four steps: 1. Mesh creation through ANSYS Workbench meshing tool. Model and physical conditions setup 3. Computation 4. Post-processing and results Two different models have been used for simulating the flow: Realizable WF (Wall Function) K- epsilon model, and SST model of Menter [3,4]. 6

7 3.1 Mesh Two- dimensional domain The discretization of the domain and the following mesh is elaborated using the FVM (Finite Volume Method). Mesh is created using the software ICEM CFD 15.0 which is integrated into the ANSYS Workbench package. For k-epsilon and SST models, two different element size discretizations have been chosen: m for k-epsilon WF, and m for SST model of Menter. Moreover the mesh for STT model has been structured in order to meet model requirements. Table 8. Mesh details. k-epsilon WF SST ItW Number of elements Number of nodes (a) (b) (c) Fig. 7. Domain discretization: a) mesh for SST model, b) structured mesh wall detail, c) mesh for k-ε wall function model. As represented in figure 7, the mesh is unstructured and coarser for the k-epsilon model (c) because large gradients of variables are not expected. The computational grid is based on tetrahedral elements. Once the domain has been meshed, the value of the skewness parameter has been checked. Mesh skewness is defined as the difference between the shape of an equilateral cell of equivalent volume and the cell in exam. Highly skewed cells can decrease accuracy and destabilize the solution. A 7

8 general rule [14] is that maximum skewness should be kept below 0.95 not to lead to convergence difficulties. The proposed mesh skewness is 0.7 hence the mesh is supposed to be reliable Three dimensional domain Simulations for a 3D domain have been performed. Mesh settings are equal to the previous D domain. The discretization counts about 1 million elements. (a) (b) (c) Fig. 8. 3D domain discretization: a) second row meshing for k-ε model, b) second row mesh for SST model, c) mesh detail for k-ε model, d) mesh detail for SST model. 3. Setup Equations needed: Energy equation (it s necessary in order to solve the temperature field, hence the density ρ) Continuity and momentum equations, provided by viscous model: Realizable k-ε and SST. As next step, steam and its properties have been defined from Fluent library. For density value, Aungier-Redlich-Kwong equation method has been used. Boundary conditions definition requires geometric selection of domain characteristic zones (inlet, outlet, wall etc ), which have been previously defined through the meshing tool. (d) 3..1 First rotor blade set Input parameters are synthesized in the following table: 8

9 Table9. First row inlet data. Mass Flow Rate [kg/s] 1. Initial Gauge pressure [Pa] X-component of Flow direction Y-component of Flow direction Turbulent Intensity (%) 5 Total Temperature [K] 713 Operating pressure [Pa] Outlet condition has been set as Pressure Outlet condition, assuming temperature invariance after nozzle expansion. Table10. First row outlet data. Gauge pressure [Pa] Total Temperature [K] 713 Periodic condition has been set for domain border and the blade edges has been considered as stationary wall. 3.. Second rotor blade set Boundary conditions on second row are the same, with exception of Inlet condition: in order to simulate a realistic behavior, the values of Outlet velocity have been extracted from first set simulation and mirrored in order to simulate the presence of the deviator blade set. All the simulations are performed with the relative velocity components w x, w y in order to obtain the same effect which would have had a dynamic wall when imposing the absolute velocity components v x, v y with reduced computational load. 3.3 Solution methods SIMPLE (Semi-IMplicit for Pressure-Linked Equations) steady-state solver has been used, which is the standard solver in Fluent software. Approximation method has been set to First Order Upwind in order to obtain a faster and more stable code. After solution convergence, all equations (Pressure, Energy, Velocity, Momentum, Turbulent Kinetic Energy and Turbulent Dissipation Rate) have been switched to Second Order Upwind so that a more accurate solution could has been achieved. The simulations have begun using the default under relaxation factors, then after switching the spatial discretization (from First Order Upwind to Second Order Upwind) they have been reduced in order to increase computational stability. Table11. Under Relaxation factors. Pressure 0.3 Density 0.8 Body forces 0.7 Momentum 0.7 Turb. Kin. Energy 0.8 Note that in Fluent Mass Flow value in inlet is referred to 1 meter of domain height, so it is not the actual mass flow in a single channel, but it had to be fixed in order to obtain the proper velocity components. For that reason in the simulation a mass flow rate of 61 Kg had to be set. s 9

10 The values in Tab.11are the ones used for the last iterations. The residuals of all the equations are monitored imposing as a convergence absolute criteria for all the equations (continuity, x- velocity, y-velocity, energy). 4. Results In the following section several results for two dimensional and three dimensional configurations, for both first and second rotor row, are represented. 4.1 First rotor row First design D simulations show some undesired flow behavior: the blade of the first rotor row (Fig.9) is affected by strong steam acceleration when leaving the channel: this is due to an excessive section reduction, which depends on blade suction side profile. In this specific situation, this is unacceptable, since relative velocity exceeds local sound velocity, creating shocks and altering velocity field in deviator inlet. Fig. 9. First attempt first row velocity field. Fig. 10. Intermediate attempt first row velocity field. Undesired acceleration in both inlet and outlet channel is shown. From this result, the first blade set profile had to be corrected. After some design attempts and simulations, as in Fig.10, a final profile has been obtained by thinning the blade both at the leading edge and at the trailing edge, and applying a different curvature. Simulation of this final profile yielded the following results (fig.11): (a) (b) 10

11 (c) (d) (c) (d) Fig. 11. Final first row: a) velocity field, b) velocity field with streamlines, c) pressure field, d) turbulent kinetic energy. The correct behavior of the flow interaction with the blade is evident from straight flow at the channel exit. Small acceleration is still present at the channel inlet, but it is subsonic and has a limited impact in blade performance. Pressure difference between suction side and pressure side is relatively small, consistently with impulse turbine operating principle. Turbulence is created at trailing edge, but it is limited in quantity and impact on dissipation. Once the final profile had been achieved, a three dimensional simulation has been performed, showing results which are slightly closer to the monodimentional analysis based on velocity triangles than the previous D results (Fig. 1). The acceleration at the inlet is clearly reduced and the outlet surface presents a smoother behaviour. As it can be seen, there is a slight radial motion (Z velocity component) near both the tip surface and the hub surface, which can be explained considering the near wall viscous effects, which obviously the D simulations are not capable to reproduce. Anyway this does not strongly affect the streamlines. 11

12 (a) (b) (c) Fig. 1. First row 3D: a) planar, b) streamlines c) radial behavior for velocity 4. Second rotor row Similarly to the process followed in first blade set design, multiple D attempts have been performed on different profiles and, after some unsatisfying results, final geometry has been obtained (Fig.13). Fig. 13. a) Final second row: streamlines and velocity field, b) turbulent kinetic energy Velocity and stream lines don t show irregular behavior, and turbulent kinetic energy is minimal in the second row wake. Three-dimensional analysis results are shown in Fig

13 (a) (b) Fig. 14 Final second row 3D:a) streamlines, b) radial behavior for streamlines. In similarity with the first rotor row there is a slight radial motion (Z velocity component) near both the tip surface and the hub surface even if it doesn t affect much the streamlines. 4.3 Comparison between expected and simulated results In order to make a comparison between the expected values from the velocity triangles and the CFD results, values at the outlet of the simulated blade are extracted and averaged in the normal direction with respect to turbine axis. Table 1. Comparison between expected and simulated results. Velocity triangles analysis [m/s] Simulated value (averaged) D [m/s] Simulated value (averaged) 3D [m/s] W W Final blade design After performing multiple D and 3D simulations on different profiles, the best performance has been obtained with the following blade shapes First row profile (a) (b) Fig. 15. Final first row: a) blade profile, b) blade model. 13

14 4.4. Second row (a) (b) 5. Conclusions Fig. 16 Final second row: a) blade profile, b) model. The design of a Curtis turbine stage has been performed from a theoretical study based on 1D velocity triangle analysis and through several blade profile improvement attempts supported by CFD feedback. Some problems in first rotor row channel design have been encountered in designing blade profiles, due to the fluid close-to-sonic relative velocity, which, with first profile attempt, tends to create shocks and strong dissipations both at channel inlet and outlet. Through profile modifications and CFD testing, better performing blade designs have been obtained; D simulations show minimal losses on first rotor blade set and acceptable losses on second rotor blade set in stand-alone simulations. 3D simulations seems to yield even better results, as dissipations are reduced and the expected radial motion is so small to be considered negligible in turbine efficiency. Nomenclature Subscripts 0 inlet nozzle 1 outlet nozzle, inlet first blade set outlet first blade set, inlet deviator 3 outlet deviator, inlet second blade set 4 outlet second blade set Quantities V absolute velocity U peripherical velocity W relative velocity V m meridian velocity V t tangentialvelocity v s local sound velocity ψ head coefficient V t /U φ flow coefficient V m /U ω angular velocity χ diametral ratio D i /D e R ρ reaction ratio δ b blade obstruction coefficient α absolute velocity angle β relative velocity angle 14

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