CC BY
73
УДК 629.735
J. Swirydczuk, M. Szymaniak
PAS Institute of Fluid-Flow Machinery, Gdansk, Poland
NUMERICAL ANALYSIS OF THE FLOW STRUCTURE IN THE RWTH AACHEN MODEL TURBINE
The paper analyses the flow through the RWTH model turbine which in the past was frequently used as the test case in ERCOFTAC studies. The flow structure is analysed numerically using two codes: FlowER and Fine TURBO Numeca. The obtained results are compared with relevant experimental data recorded in the model turbine. The analysis has made it possible to detect main secondary vortices in the flow downstream of the turbine rotor and roughly compare their characteristic parameters: strengths and position, with the real structures. The performed analysis have confirmed the potential of the used codes for qualitative studies of unsteady flow phenomena in fluid-flow machines.
Key words: model turbine, secondary flow, vortices, experiment, comparison.
1. Introduction
The analysis presented in the article refers to part of the research activity in the Institute of Fluid-Flow Machinery in Gdansk, Poland, oriented on numerical investigations of flows through turbine stages for which experimental data are well documented. These investigations aim at valuating selected numerical codes and, simultaneously, assessing the scale of activity of coherent vortex structures in their development and interaction in turbine stages. A turbine for which vast amount of experimental data is available is the 1 + 1/2 stage model turbine investigated in the laboratory of RWTH Aachen, Germany. In the past, these data were used in tests organised by ERCOFTAC on numerical analyses of the three-dimensional structure of flows through turbine stages [1].
The main numerical tool used in the investigations was FlowER, a specialised numerical code designed for analysing three-dimensional flows through stages and sections of fluid-flow machines. Its detailed description can be found in [2] and [3], among other sources. The code has an option of unsteady calculations realised using a so-called time-space periodicity, also frequently referred to as the phase lag condition. A detailed description of this condition realised by FlowER in the unsteady variant is given in [4]. In the past, FlowER was widely used in IF-FM for investigating flows through turbine stages and sections. The obtained results revealed more than good agreement with the data recorded both in model turbines, and stages of real turbines in operation in Polish and foreign power plants.
The second code used in the study was the code package FINE Turbo of NUMECA, Belgium, bought in recent years in IF-FT. A characteristic feature of this code is its orientation on turbine applications,
which made the authors expect the results revealing much higher accuracy than this presented by allpurpose CFD codes, Fluent for instance. The numerical calculations performed using these two codes for the same geometry and flow conditions provided good opportunities for evaluating the scale and nature of numerical effects on the obtained results.
2. Turbine geometry
The geometry of the analysed turbine bases on the 1+1/2 stage model turbine tested in the laboratory of RWTH Aachen, Germany. The inner diameter, Dw, and the outer diameter, DL, of the turbine are
w' ' L'
equal to 490 and 600 mm, respectively. Two stator rows in this turbine are constructed using 36 blades with Traupel profiles of 62 mm in chord length, Ck. The inlet flow to each stator row is axial and the exit flow angle is equal to 20 degrees. The rotor row consists of 41 blades with the modified VKI profiles of 60 mm in chord length, Cw . The tip clearance in the rotor row is equal to 0.4 mm. The stator and rotor rows have radial blades with constant cross-sections. The reference line in the stator is situated at the blade trailing edge, while in the rotor — in the blade mass centre.
The rotational speed of the turbine rotor is 3500 rev/min, and the relative rotor inlet and exit angles are equal to 49.3 and 151.2 deg, measured with respect to the circumferential direction.
3. Grid and thermodynamic data
The FlowER calculations made use of the H-type grid with the boundaries between the passages situated on blade surfaces. The approximate numbers of grid nodes for stator K1 and rotor W were equal to 1.6 million, while for stator K2 is was equal to 2.2 million.
© J. Swirydczuk, M. Szymaniak, 2011
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Profiles
Fig. 1. Geometry of 1 + 1/2 stage RWTH Aachen turbine (left) and the shapes of stator and rotor blades (right)
The grid refinement in the boundary layer secured obtaining the y+ level of an order of 25 in all directions.
A sample arrangement of gridlines in the stator and rotor rows is shown in Fig.2, for the second refinement level. The upper figure shows the gridline pattern in the meridional plane x0z, while the lower figure — in the circumferential plane y0z.
Fig. 2. Sample arrangements of gridlines in stator and rotor passages — Flower (level II)
Fig. 3. Calculation grid in the turbine passage mid-span section - Fine TURBO (level II)
The code Fine TURBO uses the grid of HOH type, in which the blade is in the centre of the flow area, and the central line of the flow passage is the periodicity border. The approximate numbers of grid nodes for all rows were equal to 2.0 million. A sample grid for Fine TURBO calculations is shown in Fig. 3.
The thermodynamic data assumed in the calculations based on the experimental data recorded in this turbine [1]. In the inlet plane these data have the form of the distributions of total pressure, P0c, total temperature, 70c, and inlet flow angles: a in circumferential plane, and / in meridional plane, at seven points along turbine passage radius R. The average values of those parameters were: P0c = 0.1677e6[Pa], T0c = 307.8[K], a0 = 0[deg] and /0 = 0[deg] (axial inflow).
The parameter assumed at the turbine exit was the static pressure, P2, the distribution of which was defined at 14 points (FlowER) or 7 points (Fine TURBO) along the turbine passage radius, for the average value of P2 = 0.1085e6[Pa].
The FlowER calculations made use of the Menter's k-w SST two-equation differential turbulence model, while the Fine TURBO calculations were performed using the Spalart-Allmaras single-equation differential model of turbulence.
4. Comparing the calculated results with the experimental data
The sequence of figures in this section makes the basis for comparing the distributions of selected flow parameters in characteristic turbine passage sections which were calculated using the codes FlowER and Fine TURBO with those obtained experimentally by Walraevens and Gallus in the model turbine [5].
Figure 4 shows the distributions of secondary velocity vectors experimentally recorded in the measuring plane downstream of the rotor exit — section 2 in Fig.1(right) [5]. The authors of the experiment made an attempt to extract from these distributions vortex structures which are commonly
observed in turbine passages. The basic structures are two passage vortices situated close to the outer (upper) and inner (lower) passage walls. The upper passage vortex (1) has the clockwise rotation, while the lower vortex (2) is of opposite rotation direction. Moreover, the authors indicate the presence of much weaker vortices: the trailing shed vortex (3) and the leakage vortex (4), as well as secondary flows (5) generated by the rotor wake.
the upper passage wall, while the lower, more intensive vortex (2) is recorded at a slightly larger distance form the lower passage wall. In the second characteristic time interval, here represented by time ¡/7=20/32, the vorticity corresponding to passage vortices has two centres situated one above the other, which suggests the absence of one regular vortex structure in this case. In turn, in the third group of diagrams, with time ¡/7=28/32 as the representative, the vorticity centres situated closer to the midspan plane disappear and the only active centres are those recorded close to the upper and lower passage walls.
Fig. 4. Secondary velocity vectors downstream of the rotor in the rotating reference system [5], / =1.148: 1 — upper
rotor passage vortex, 2 — lower rotor passage vortex, 3 — trailing shed vortex, 4 — leakage vortex, 5 — secondary flow
The below presented comparison of the numerical results with the experimental data aims at detecting most intensive passage vortices (1) and (2), by searching, in the area of interest, for vortices revealing characteristic rotation direction.
Figure 5 shows selected secondary velocity vector distributions obtained from FlowER calculations in the plane corresponding to the measuring section. Such distributions were recorded at certain times t during the period T of the relative rotor/stator blade motion. Each presented velocity vector distribution is complemented by a corresponding entropy distribution recorded at the same time in the analysed section.
The behaviour of the secondary vortices during the entire time period T can be divided into three sub-intervals. Initially, the vortices with the rotations corresponding to those of the passage vortices are situated in the places close to those recorded experimentally - compare time t/T=8/32 in Fig. 5 and Time Index 33 in Fig.4. The upper passage vortex (1), of lower strength, is situated at a distance approximately equal to 10% of passage span from
t/T = 28/32
Fig. 5. FlowER: velocity vectors and entropy distributions downstream of rotor exit — rotating coordination system,
z/czr= 1.136
t/T = 14/20
Fig. 6. Fine TURBO: velocity vectors and entropy distributions downstream of rotor — rotating coordination system, z/czr= 1.136
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Figure 6 shows the results obtained from Fine TURBO calculations, for /1=14/20. Like for FlowER, the secondary velocity vectors presented on the left reveal two large and regular vortex structures, which after comparing with the experiment are identified as the rotor passage vortices. In other diagrams, not shown here, also some traces of activity of the passing stator vortices can be occasionally observed, but the pattern of their behaviour is rather unclear. The entropy distributions on the right also reveal two centres of enhanced vorticity corresponding to the positions of the rotor passage vortices. The distribution of flow parameters shown in this figure is less concentrated and the secondary structures occupy larger part of the passage than in FlowER calculations. On the other hand, these structures seem to be more stable than those generated by FlowER. Generally, the instantaneous flow patterns produced by Fine TURBO can be interpreted as closer to the experiment, although the fact that the experimental data were recorded in early ninetieths of the last century makes it difficult to assess to which extent the then-recorded level of vorticity dissipation was affected by the resolution of the recording instruments used.
height from the lower passage wall (i.e. higher than it was suggested by the secondary vector distributions). The upper passage vortex is situated closer to the corresponding wall, and the local Mach number minimum is situated slightly to the left with respect to the lower vortex. In general, the flow patterns in the corresponding diagrams are more similar to each other than in the case of secondary velocity vectors.
20/32
28/32
Fig. 8. FlowER — Mach number distributions downstream of rotor in rotating reference system, z/cr= 1.136
t/T = 14/20
Fig. 7. Mach number distributions downstream of rotor in rotating reference system [5], z/czr=1.148
Figures 7 to 9 show Mach number distributions experimentally recorded and numerically calculated in the same measuring section No. 2 downstream of the rotor. Here again, comparing those diagrams is of purely qualitative nature and is done by comparing positions and shapes of the areas occupied by the vortices. In the experimental diagram these areas are marked dark, while in their numerical counterparts — using green-to-blue colours for increasing Mach numbers.
Comparing the experimental Mach number distributions, Fig. 7, with those obtained from FlowER calculations, Fig. 8, reveals certain similarities. The shape of the lower passage vortex is elongated, with the centre situated at a distance of 30-40% of passage
Fig. 9. Fine TURBO — Mach number distribution downstream of rotor in rotating reference system, z/cr = 1.136
The results obtained from Fine TURBO calculations also reveal similar flow structure. Like in previous diagrams, clearly visible is the Mach number minimum approximately situated at the position of the lower rotor passage vortex, and the second, slightly weaker minimum close to the upper passage wall. Like for the entropy, the Mach number distributions obtained from Fine TURBO calculations are smoother less concentrated than the FlowER distributions.
Conclusions
The numerical analysis of the flow through the RWTH Aachen model turbine has made it possible to detect and recognise basic secondary vortices in the selected measuring section of the turbine, downstream of the rotor. Remarkable qualitative agreement between the numerical calculations and experimental data was obtained for Mach number distributions. The secondary vector and entropy distributions revealed larger differences, the origin of which can be both on the numerical, and
experimental side (errors in recording unsteady flow data).
One of the questions which the reported study was expected to answer was to which extent the numerical analyses performed using contemporary CFD codes can capture unsteady phenomena taking place in stages of real fluid-flow machines. The results obtained using computers and numerical parameters within the ranges well available in research centres and design offices dealing with fluid-flow machinery issues make it possible to answer this question positively. Contemporary CFD codes are reliable practical tools, providing opportunities for realistic qualitative prediction of unsteady flow phenomena in fluid-flow machines. Unfortunately, finding reliable experimental data describing in detail the real course of these phenomena is extremely difficult and this fact makes more precise evaluation of the agreement between the numerical and experimental results very difficult, especially in quantitative aspect.
References
1. ERCOFTAC Test Case 6, 1-1/2 STAGE AXIAL FLOW TURBINE [Электронный ресурс] / Institut fur Strahlantriebe und Turboarbeitsmaschinen (1ST) RWTH Aachen,
Germany. — 2011 — Режим доступа : WWW.URL: www.ercoftac.org.
2. Yershov S.V., The application package FlowER for the calculation of 3D viscous flows through multistage machinery / S.V.Yershov, A.V.Rusanov // Certificate of state registration of copyright, ПА №77, Ukrainian state agency of copyright and related rights, Kiev, 19.02.1996.
3. Numerical Simulation of 3D Flow in Axial Turbomachines / S.V. Yershov, A.V. Rusanov, A. Gardzilewicz, P. Lampart, J. Swirydczuk // TASK Quarterly - 1998. - Vol. 2, № 2. - P. 319-347.
4. Rusanov, A.V. Simulation of 3D Unsteady Viscous Flow Generated by Interaction of Reciprocally Moving Turbomachine Cascades / A.V.Rusanov, S.V.Yershov // Modelling and Design in Fluid-Flow Machinery, Badur, J. et al eds. — Wyd. IMP PAN. - 1997. - P. 153-160.
5. Walraevens R.E. Three-Dimensional Structure of Unsteady Flow Downstream the Rotor in 1 x Stage Turbine / R.E.Walraevens, H.E.Gallus // Unsteady Aerodynamics and Aeroelasticity of Turbomachines, Y. Tanida and M. Nuba (editors). -Elsevier Science. 1995. - P. 481-498.
Поступила в редакцию 30.05.2011
G. Шв1ридчук, M. Шиманяк. Числовий анализ структури потоку в модельнш Typörni RWTH Aachen
Уcmammiрозглядаеться течш через модельну турбту RWTH, яка в минулому неодноразово використалась як контрольний приклад долджень ERCOFTAC. Структура потоку до^джуеться чисельно з допомогою двох програм: FlowER та Fine TURBO Numeca. Результати порiвнююmьcя з вiдповiдними експериментальними даними, що отримаш для модельно1 турбти. Aнaлiз дозволив виявити основы вторинш вихри в течи за ротором турбти i наближено порiвняmи ïx характеристичш параметри: ттенсившсть та мсцез-находження, з реальними структурами. Проведене до^дження тдтвердило можливоcmi використаних програм щодо яксного вивчення явищ при нестацюнарнш течи в турбома-шинах.
Ключов1 слова: модельна турбта, вторинш течи, вихри, порiвняння з експериментом.
Е. Швирыдчук, M. Шыманяк. Численный анализ структуры потока в модельной турбине RWTH Аа^еп
В статье рассматривается течение через модельную турбину RWTH, которая в прошлом неоднократно использовалась как контрольный пример исследований ERCOFTAC. Структура течения исследуется численно с помощью двух программ: FlowER и Fine TURBO Numeca. Результаты сравниваются с соответствующими экспериментальными данными, полученными для модельной турбины. Анализ позволил обнаружить основные вторичные вихри в течении за ротором турбины и приближенно сравнить их характеристические параметры: интенсивность и положение, с реальными структурами. Проведенное исследование подтвердило возможности использованных программ для качественного изучения явлений при нестационарном течении в турбомашинах.
Ключевые слова: модельная турбина, вторичные течения, вихри, сравнение с экспериментом.
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