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Session: Turbo expanders I
Session starts: Tuesday 08 October, 11:20
Presentation starts: 12:00
Room: Van Weelde Zaal

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Piotr Klonowicz (Universität Bayreuth, Zentrum für Energietechnik, Lehrstuhl für Technische Thermodynamik und Transportprozesse)
Dieter Brüggemann (Universität Bayreuth, Zentrum für Energietechnik, Lehrstuhl für Technische Thermodynamik und Transportprozesse)

Abstract:
INTRODUCTION Small power turbines are governed by the same physical principles as the big ones. However, due to mainly practical reasons their designs are very different. It is usually not profitable to apply sophisticated designs such as complex geometry or many stages in case of a small power machines (Turunen-Saaresti et al., 2011). It is also much more difficult to maintain the same relative clearances, chords and other important dimensions (Macchi and Predichizzi, 1981). This is one of the reasons why turbines designated for distributed generation have low efficiencies. Another reason is a consequence of the Reynolds number influence. When specific speed is small a simple way of minimizing the secondary losses and increasing the efficiency is to apply partial admission. It is also possible and recommended to apply the known correlations for the passage loss and partial admission loss to obtain optimized stage kinematics and size (Lozza and Macchi, 1986). Here, however, some problems in regard to the use of correlations arise. First of all, amongst various loss correlations significant discrepancies both in the physical assumptions and results occur, in particular in the context of partial admission. For example Traupel (2001) suggests that the main source of loss comes from both rotor blade pumping (windage) in the inactive sector and end-sector loss. On the other hand, Yahya and Doyle (1969) neglect the blade pumping loss in their correlations, they also state that blade pitching is of very little significance which is in clear contradiction to the relations given in other literature (Glassman, 1975). Thus, there is no universal correlation for the partial admission loss. What is more, partial admission may cause unforeseen excitation frequencies, with potential deterioration of the machine durability (Fridh, 2012). The development of the CFD codes allows scientists and engineers for a deeper insight into the phenomena occurring in various types of turbomachinery. For example, the modern codes enable simulation of supersonic turbine stages operating with real gases (Harinck et al., 2011; Klonowicz and Hanausek, 2011) and even their optimization (Pasquale et al., 2011). In spite of this fact, simulating the partial admission is still a challenging problem. The reason for that is twofold. First of all, there is, in general, lack of periodicity in such stages and thus it is recommended to simulate the whole stator and rotor blade rows. Additionally, the flow in the partial admission stage, especially near the end-sectors reveals strong unsteadiness (Fridh, 2012; Hushmandi, 2010). Thus, transient simulation is needed. All of this leads to very time consuming numerical tasks. ASSUMPTIONS In order to reduce the computational costs one often applies simplified models. One method of simplification is to diminish the three-dimensional computational domain into a two-dimensional one, for example in the blade-to-blade plane. Such approach allows us to compute much more cases and in case of partial admission it produces quantitatively correct results (Hushmandi, 2010). Besides the questionable reliability of two-dimensional CFD models there is a humdrum problem associated with them – the geometry must be suitable for such analysis. Most of the turbine designs are not suitable for straightforward two-dimensional analysis because of overlaps and non-zero flaring angles etc. Thus, in order to investigate a turbine in 2D, one should redesign it or even prepare a new, dedicated design. As shown in Hushmandi (2010) it is relatively easy to adopt an axial-flow turbine for such simulation – it requires cylindrical hub and shroud surfaces. In case of a centripetal turbine both the hub and shroud surfaces must be normal to the axis of rotation. In this configuration the channel naturally converges and that results in distorted stage kinematics, especially for relatively big rotor blade chords. What is more, the rotor domain should be extended further in order to properly place the boundary conditions and to avoid recirculation at the boundary. Therefore whole centripetal stages are not, in general, suitable for two-dimensional simulations. One of possible solutions of these drawbacks leads through designing a centrifugal stage as its passage area naturally increases with the flow direction. These kinds of stages are known for example from Ljungstrom-like designs and recently have been investigated for ORC applications (Pini et al., 2011). Impulse centrifugal stages (suitable for partial admission application) are generally avoided, mainly due to relatively low specific work, some research is available in the literature (Cho et al., 2011). In the presented work a centrifugal impulse stage was designed specially to enable 2D numerical simulations in the blade-to-blade plane. The turbine is designated to work with cyclopentane with expansion ratio of 20 and an absolute back pressure of 1.1 bar. The design rotational speed was set to 30,000 rpm. The nozzle divergent part was designed in a way to provide the expansion to the design stator outflow pressure and the blade angles at the outflow correspond to the predicted average flow direction. The rotor blade angles at inlet and outlet also correspond to the calculated flow directions and the flow channels between the blades have constant width. The geometry of the stage is presented on Figure 1. Figure 1: Centrifugal stage operating with cyclopentane. CFD ANALYSIS The numerical analysis was made with the application of the commercial code Ansys CFX, v. 14.0. The numerical model was similar to that applied by Harinck et al. (2011), except for the fact that every case was computed as an unsteady simulation with 30 time steps per one rotor blade pass and maximally 10 coefficient loops. The cyclopentane was modeled as a real gas by means of tabularized thermodynamic properties (REFPROP). The applied boundary conditions include the total parameters at the inlet (pressure and temperature) and the average static pressure at the outlet. Their values were consistent with the design point. As the turbulence model SST k-ω was selected. The computational domains consisted of about 0.5 million nodes. The average resutling Courant Number was 5.3. The turbine was simulated with different partial admission sizes and different partial admission configurations to investigate the influence of the admission size on the efficiency and to identify the extents of the impact of pumping loss and end-sector loss, Figure 2. Every configuration of the partial admission was simulated in two variants: with one-side casing rotor and two-sides casing rotor, Figure 3. The presented figures show also the entropy and pressure fields which allow for a qualitative assessment of the flow and to identify, for example, where the mixing takes place. Figure 2: Different configurations of partial admission with the resultant entropy fields (statistically converged values). Figure 3: One-side rotor casing and both-sides rotor casing with the resultant pressure fields (statistically converged values), reference pressure equal to 1 bar. According to the numerical model the use of on both sides of the rotor yields a significant efficiency benefit over a one-side casing solution. This result is consistent with the literature data (Glassman, 1975; Traupel, 2001). With two-side casing it is possible to maintain high efficiency even if the admission size is around 0.1. In case of one-side casing efficiency decreases much more considerably, Figure 4. What is more, rotor casing reduces not only the pumping loss but also the end-sector losses. Figure 4: Efficiency change with the degree of partial admission. CONCLUSIONS The simulations show that it is possible to obtain stable 2D blade-to-blade unsteady numerical solutions of flow fields in supersonic turbines working with real gases. Such simulations may be helpful in finding optimal admission rates for small scale turbines operating with organic vapors as they allow one to investigate a significant amount of cases in reasonable time. The 2D model has obvious limitations and in future should be compared with its 3D equivalent to investigate its reliability. In further work also different stage specifications have to be checked such as different blade pitches, different chord sizes and various blade angles. The presented design shows a promising performance which in further work will be compared with equivalent centripetal stages. LITERATURE Cho, S., Ahn, K., Lee, Y., 2011. Performance Characteristics of a Partially Admitted Small-Scale Mixed-Type Turbine. Int. J. Turbo Jet-Engines 28, 299–307. Fridh, J., 2012. Experimental Investigation of Performance, Flow Interactions and Rotor Forcing in Axial Partial Admission Turbines. PhD Thesis, KTH, Stockholm, Sweden. Glassman, A.J., 1975. Turbine design and application. Scientific and Technical Information Office, National Aeronautics and and Space Administration: [For sale by the Supt. of Docs., U.S. Govt. Print. Off.]. Harinck, J., Pasquale, D., Pecnik, R., Colonna, P., 2011. Three-Dimensional RANS Simulation of a High-Speed Organic Rankine Cycle Turbine, in: First International Seminar on ORC Power Systems ORC 2011. Delft. Hushmandi, N.B., 2010. Numerical Analysis of Partial Admission in Axial Turbines. PhD Thesis, KTH, Stockholm, Sweden. Klonowicz, P., Hanausek, P., 2011. Optimum Design of the Axial ORC Turbines with Support of the Ansys CFX Flow, in: First International Seminar on ORC Power Systems ORC 2011. Delft. Lozza, G., Macchi, E., 1986. Comparison of Partial Vs Full Admission for Small Turbines at Low Specific Speeds. International journal of turbo and jet engines 3, 307–317. Macchi, E., Predichizzi, A., 1981. Efficiency Prediction for Axial-Flow Turbines Operating with Nonconventional Fluids. Journal of engineering for power 4, 718–724. Pasquale, D., Ghidoni, A., Rebay, S., 2011. Shape Optimization of an ORC Radial Turbine Nozzle, in: First International Seminar on ORC Power Systems ORC 2011. Delft. Pini, M., Persico, G., Casati, E., Dossena, V., 2011. Preliminary design of a centrifugal turbine for ORC applications, in: First International Seminar on ORC Power Systems ORC 2011. Delft. Traupel, W., 2001. Thermische Turbomaschinen. Springer Singapore Pte. Limited. Turunen-Saaresti, T., Uusitalo, A., Honkatukia, J., Larjola, J., 2011. Effects of Turbine Efficiency to Small-Scale ORC Process Electricity Production and Profitability, in: First International Seminar on ORC Power Systems ORC 2011. Delft. Yahya, S.M., Doyle, M.D.C., 1969. Aerodynamic losses in partial admission turbines. International Journal of Mechanical Sciences 11, 417–431.