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M. Szymaniak , A. Gardzilewicz, M. Karcz, J. Swirydczuk CIRCUMFERENTIAL ASYMMETRY IN FLOWS THROUGH STEAM TURBINES 1. INTRODUCTION The steam flow trough a turbine is extremely complex and difficult for analysing. One reason for that is complicated geometry of the blade systems of both unmovable stator rows and moving rotor rows, which cooperate with other apparatuses within the framework of the power station thermal cycle. Another reason lies in difficulties with modelling physical phenomena taking place in the discussed flow. Steam expansion in the turbine is executed at high and low thermodynamic parameters, and at different velocities. The flow is highly turbulent with the presence of intensive vortices, shock waves and phase transitions. That is why the design methods used in the past in turbine designs were simplified. For instance, thermal and flow calculations are as a rule conducted using Eulerian methods in 1D and 2D models, to which relevant corrections, calculated from experiments, were introduced to the conservation equations to take into account fluid viscosity. 3D model based modern RANS codes are used rather rarely, preferably for analysing new pilot constructions, or elements of most complicated geometry of feeding systems, seals, etc. As a rule, design calculations neglect the permanent and unavoidable circumferential asymmetry of the flow through the turbine. This is partially justified, as the experiments, the overwhelming majority of which was performed on model stands in the past, have revealed that power losses generated in the turbine by this asymmetry are small [1],[2]. Moreover, numerical calculations oriented on taking into account circumferential flow asymmetry turned out to face limitations connected with unrealistically long times of computations performed on fully modelled 3D geometry of turbine components, rather than with pure physics of the flow[3], [4]. Circumferential asymmetry of the flow through a steam turbine is closely related with its construction, which is schematically shown in Fig. 1. Fig. 1 Schematic of steam flow through a turbine: 1 - inlet, 2 - flow extraction, 3- exit. The schematic reveals that the circumferential flow asymmetry at turbine inlet results from the change of steam flow direction, while that inside the turbine is caused by the flow of steam extracted through one or two pipes. The exit asymmetry is a consequence of the structure of the exhaust hood in which the flow of steam dramatically changes direction from horizontal at turbine exit to vertical near the condenser. In the paper, circumferential asymmetry of the turbine flow is an object of performance analysis, based on a selected 200 MW turbine operating in nominal conditions. The calculations were performed using RANS codes, the results of which were verified on the data recorded in experimental investigations of turbine exits and regeneration stages, done by research teams of Diagnostyka Maszyn and the Institute of Fluid-Flow Machinery [5, 6]. 1 Analysing circumferential asymmetry of the flow at turbine inlet is most difficult, in particular when the nozzle-group control is in use and, during partial turbine load, particular valves connected to the nozzle boxes along the turbine perimeter have different levels of opening. 2. CIRCUMFERENTIAL ASYMMETRY OF FLOW THROUGH THE TURBINE LAST STAGE AND EXHAUST HOOD Difficulties in precise calculation of flow through turbine last stages taking into account its circumferential asymmetry result from the fact that in this case the geometry of a collection of small-scale last stage passages is to be linked together with the much larger-scale geometry of the exhaust hood. That was why a simplified methology was applied for studying circumferential flow asymmetry in this turbine part [5]. This methodology couples together, in an iterative manner, the calculations of the flow through the turbine last stage with those concerning the exhaust hood, see Fig.2. FIG. 2 Coupled calculations of the turbine last stage/exhaust hood flow. Exhaust hood inlet flow parameters are assumed on the coupling plane or in the overlapping area, based on the turbine last stage calculations. In the first part of the iteration loop the flow in the turbine last stage was calculated using the initial values of the inlet parameters and the mass flow rate. These calculations were performed assuming circumferential symmetry of the flow through the last stages, which made it possible to simplify the calculation area to one passage in each of four rows composing the two last stages. The obtained uniform distributions of total parameters at turbine exit were then used as the input data for the exhaust hood calculations on a plane coupling these two calculation domains, see Fig. 2. In the second part of the first iteration loop, the flow through the asymmetric exhaust hood was calculated assuming constant pressure at exhaust hood exit, an effect recorded in past measurements. In the exhaust hood the flow changes direction by 90 o, which is a source of circumferential flow asymmetry, manifesting itself, for instance, in the asymmetric shape of static pressure at turbine exit, see Fig. 3. FIG.3 Radial and circumferential distributions of static and total pressure at turbine exit. 2 The information on this distribution was then used in the second iteration loop calculations, which this time were done for a number of separate turbine stage passages situated around the turbine perimeter. For each passage, the assumed exit pressure corresponded to that obtained in the exhaust hood calculations for this stage location. In practice, the most effective results were obtained using 6 passages uniformly distributed along the turbine perimeter, see Fig. 3. The last stage and exhaust hood calculations composing consecutive iteration loops were repeated until satisfied convergence of the circumferential static pressure distributions generated individually by the last stage calculations and the and exhaust hood calculations was obtained. The measure of the convergence is defined as: 1 n p m ,i p m ,i 1 tol n11 p m ,i where: Pi –static pressure on the coupling plane m- number of calculation segments along the perimeter i - number of iterations It is noteworthy that the presented methodology, when applied to the LP turbine, takes also into account strong changes of parameters along turbine radius, as resulting from the presence of leakage flows over unshrouded rotor blades. The calculations were performed using specialised CFD codes: FlowER [6] and Fluent [7], which had been earlier tested on available experimental material. Specially prepared numerical procedures secured automatic data transfer between these two codes. The calculations were performed on structured and unstructured grids. In total, they had only 2.5 million nodes, see Figs. 4 and 5 [5]. The computing time for the realisation of one iteration calculations did not exceed ten to twenty hours on an available PENTIUM computer. FIG. 4 Structured grid used in turbine stage calculations [5]. 3 FIG.5 Structured and unstructured grid used in exhaust hood calculations [5]. Of high importance is that the thermodynamic data for the calculations were taken from thermal measurements done on a real turbine in operation [5]. The research rig, with marked measuring points, is shown in Fig. 5, while Fig. 6 shows probes used in the measurements. FIG.6 Distribution of probes in the blade system of LP part turbine: a) meridional section, b) cross section, c) general view, [8]. 4 FIG. 7 Plate probe for thermal and flow measurements, along with the optical system Complicated structure of the circumferentially asymmetrical flow through the exhaust hood is clearly visible from the obtained results of calculations. Figures 8 and 9 show a sample distribution of streamlines in the exhaust hood chamber, and the velocity fields recorded in selected exhaust hood cross sections. FIG.8 General streamline pattern of the steam flow in the turbine exhaust hood [7]. 5 FIG.9 Velocity fields inside 360 MW turbine exhaust hood [7] The next figure, Fig. 10, shows typical circumferential static pressure distributions recorded on the coupling plane in consecutive iterations. The static pressure differences recorded between the last stage (constant value - stage calculations) and the exhaust hood inlet (exhaust hood calculations) were as high as 20%. When assuming the pressure convergence margin equal to 3%, the convergence of the two solutions was reached after three iterations. FIG. 10 Comparison of circumferential static pressure distribution obtained in iteration I, II and III (mid-span section). The calculated circumferential asymmetries of static pressure distributions along the turbine perimeter well corresponded with the results of measurements recorded at six points uniformly distributed along the turbine exit [10]. It is noteworthy that in temperature calculations the differences resulting from circumferential asymmetry were negligibly small < 0.3oC, and, in fact, beyond experimental verification. The performed numerical calculations made it possible to assess the level of energy losses attributed to flow asymmetry in the turbine. Static pressure changes recorded at the upper part of the flow passage and compared with the averaged pressure turned out to shift the last stage efficiency by as little as 0,5%, which is negligible when referred to the efficiency of the turbine as 6 a whole. Higher losses were recorded in the exhaust hood, which resulted not only from rapid flow direction changes in this area, but also from blocking the flow to the condenser by intensive leakage jets over unshrouded last stage rotor blades, see Fig. 11. These leakage flows are observed in this turbine part at velocities reaching 400m/s. The course of this thermodynamic process in the exhaust hood is schematically shown in Fig. 12. FIG.11 Velocity vectors in 200 MW turbine behind the last stage: a) turbine calculation, b) exhaust hood calculation . FIG. 12 Definition of kinetic energy loss coefficient in the turbine exhaust hood Due to throttling of the flow in the exhaust hood, the pressure pk recorded in the condenser is lower than that directly downstream of the turbine pwyl, which is equivalent to extra energy loss H, determined from 3D calculations and verified in measurements. The resultant efficiency losses, related to total enthalpy drop during steam expansion in the 200 MW turbine LP part, were assesses as equal to 3%. This efficiency change reduced the turbine power output by 300 kW, which is 6 times as much as the losses generated by the circumferential flow asymmetry inside the blade system of the turbine operating in nominal conditions. 2.2. REGENERATIVE EXTRACTION STAGE For analysing circumferential asymmetry of the steam flow through the turbine with steam extraction, an iterative method similar to that described above was applied [12]. This time again, the main motivation was to minimise the computing time. A scheme of this methodology, slightly modified with respect to that described above, is given in Fig. 13. 7 Fig. 13. Scheme of realisation of calculation iterations in the coupling plane methodology applied to the flow through the regenerative extraction stage. In this case the calculations of flow through two turbine stages, one located directly in front of and one directly behind the diffuser, were coupled with those concerning the diffuser itself and the extraction chamber. The coupling planes were situated between the diffuser and the stages, at diffuser inlet and exit. In the first iteration step the flow through the stages was calculated assuming its circumferential symmetry. Circumferential irregularity in the distribution of flow parameters around the diffuser perimeter was generated by asymmetrical steam extraction via one pipe to the extraction system. The resultant non-uniform pressure distribution was used in the second step of stage flow calculations. In this case the stage was divided into six sections uniformly distributed along stage perimeter, see Fig. 13. Pressure differences recorded in this case were much smaller than those obtained for the exhaust hood. The rate of convergence of iterations was checked by tracing circumferential distribution of the mass of steam flowing into the extraction opening, according to the criterion: 1 n M m ,i M m ,i 1 tol n i 1 M m ,i where: M – extraction mass flow rate m- number of calculation segments i – number of iterations The calculations were performed for the 200 MW turbine, using as the calculation domain two stages and the first regenerative extraction chamber in the LP turbine part. Sample grids used in FlowER and Fluent calculations are shown in Figs. 14 and 15, in total they included 1.800 000 nodes. The values of the thermodynamic parameters were taken from thermal measurements, a detailed report on which is given in [10]. A complete set of these measurement results has made it possible to check credibility of both the calculated distributions of the remaining thermodynamic parameters in selected sections in which the measurements were done, and the calculated mass flow rate of the main flow and the extraction flow. 8 FIG.14 Calculation grids for turbine stages FIG.15 Calculation grids for diffuser with extraction chamber and pipe The streamlines and velocity distributions illustrating circumferential asymmetry in selected diffuser cross sections are shown in Figs. 16 and 17, (more details can be found in [12]). FIG.16 Streamlines in the interstage diffuser and the extraction chamber with pipe fragment 9 FIG. 17 Pressure distributions in selected cross sections Mass distributions of the flow taken by the extraction system in particular iterations are shown in Fig. 18, for a simplified diffuser geometry. The expected pressure convergence at the level of 3% was obtained as early as after the third iteration. The entire time of computations performed on the Pentium computer was between ten and twenty hours. FIG. 18 Distributions of mass flowing from the turbine to the extraction chamber in successive iterations Figure 19 shows sample distributions of thermodynamic parameters at diffuser inlet and exit, which were obtained in more precise calculations. When the parameters in front of and behind the calculated stages were assumed constant, changes of parameters in circumferential distributions inside the diffuser were small. The flow calculations took into account intensive leakage flow with angular momentum above the unshrouded rotor blade. This flow was a source of additional asymmetry in the distribution of mass flow rate inside the extraction chamber, which can be noticed when comparing results of calculation with and without leakage flow (Fig. 20) 10 FIG. 19 Parameters at interstage diffuser inlet and exit, for Gex = 1[kg/s] Fig. 20 Circumferential distribution of mass entering the extraction chamber a) with leakage flow b) without leakage flow Efficiency changes of the turbine stage provoked by circumferential flow asymmetry, treated as a function of the main flow related mass flow rate of the extraction flow, are given in Fig. 21. As can be noticed, when the extraction flow reaches as much as 6% of the mass flow rate of the total flow, the efficiency decrease of the stage adjacent to the diffuser does not exceed 1%. This result 11 was confirmed in experimental investigations performed by Garkusza on model turbines [1]. When the mass flow rate of the extraction flow is lower, the turbine stage efficiency decrease does not exceed 0.3%. FIG.21 Efficiency of the stage behind the diffuser vs. mass flow rate It is noteworthy that similar distributions of mass and thermodynamic parameters were recorded for verifying calculations done using Fluent, in which the complete geometry of the turbine stages, including all blades, and the extraction system area were modelled. Here, due to computer restrictions, the total number of nodes in the grid describing the geometry was limited to 4 mln. Even for such a coarse model, the computing times were longer by an order in magnitude than those recorded using the above described iterative method. Detailed assessment of stage energy losses was not possible in this case. 3. CONCLUSIONS The performed calculations have proved that circumferential changes in steam parameters along the turbine inlet, exit, and extraction area, are small. Relative pressure changes along turbine perimeter did not exceed 0.5%, and were accompanied by practically negligible temperature changes. All this results in very small decease of exit stage efficiency. For the last stage of the LP turbine, those losses do not exceed 1%, which is completely negligible when referred to the efficiency of the entire turbine. The energy losses generated during the flow through the exhaust hood, in which the steam changes direction by 90 degrees ( from circumferential to radial), are larger. A direct reason for this is the pressure rise behind the turbine which results from the blockage of the flow to the condenser by intensive leakage flow leaving the last stage. Energy losses attributed to this effect depend on the design of the exhaust hood, but do not exceed 1% for the entire turbine. Circumferentially asymmetric steam extraction from the turbine to the regeneration system exerts limited impact on non-uniformities of the main steam flow in the turbine. The mass flow rate non-uniformities can be most of all recorded in the extraction chamber and, as relevant calculations have proved, can reach even as much as 50%. When the mass of the flow extracted to the regeneration system is at the level of about 2%, pressure changes observed in the blade system do not exceed 0.5%, which has practically no effect on turbine efficiency. Higher efficiency decrease is recorded for the stage downstream of the extraction point when the extraction mass flow rate is higher than 10%, which can take place in turbines from which the steam is extracted for heating purposes. The circumferential flow asymmetry is the highest at turbine inlet, in particular in turbines with nozzle-group control system, when different openings of inlet valves in nozzle boxes around the control stage perimeter are a source of additional asymmetrical flow. Due to computer limitations, energy losses attributed to flow asymmetry at turbine inlet and control stage have not been assessed in detail so far. This work is in progress now. 12 4. REFERENCES 1. Garkusza A.W.: Aerodinamika protocznoj czasti, Izd. Maszinostrojenije, Moskwa 1983. 2. Zariankin A.E., Simonov B.P.: Wychlopnyje patrubki parowych i gazowych turbin, Izd. MEI, Moskwa 2002 3. Daves W.N.: Current future developments in turbomachinery CFD, Proc. 2th European Conference on Turbomachinery Fluid Dynamics, Antverpen, 1997. 4. Kiciński J. and other: Modelling and diagnostics of mechanical and aerodynamic interactions in power turbosets, IF-FM Publishers, Gdansk, 2005 (in Polish) 5. Gardzilewicz A., Marcinkowski S.: Diagnosis of LP steam turbines: prospects ogf measuring technique, ASME JPGC, vol 3, 1995. 6. Gardzilewicz A.: Performance analysis of regenerative extractions of turbine based on thermodynamic measurements in power plants, VDI Verlag Berichte 1186, Proc. 1st European Conference on Turbomachinery Fluid Dynamics, Erlangen, 1995. 7. Gardzielwicz A., Swirydczuk J., Badur J., Karcz M.: Methodology of CFD computations applied for analysing flow through steam turbine exhaust hood, Transactions of IF-FM, vol. 114, Gdansk 2003, pp. 19-36. 8. Gardzielwicz A., Marcinkowski S.: Results and protocols of measurements of thermal steam flow parameters in LP part of 18K-370 turbine, block No. 10, Diagnostyka Maszyn Report, Gdansk 1999/2000 (in Polish) 9. Szymaniak M.: CFD calculations of steam turbine stages with regenerative extraction, Systems - Journal of Transdisciplinary Systems Science, vol. 11, No. 1 pp. 292-299, 2006. 10. Marcinkowski S., Gardzilewicz A.: Results and protocols of measurements of kinetic steam flow parameters in LP part of K-200 ND37 turbine block No. 8 in Turow Power Plant, Diagnostyka Maszyn Report, Gdansk 1997 (in Polish) 11. Szymaniak M.: The application of CFD technique for calculating steam turbine stages with leakage and regenerative extraction flows, Ph.D. thesis, Gdansk, 2008. 13