The turbine stage performance simulation needs a total loss coefficient to be assessed, comprising the losses coming from both profile and end-wall surfaces, through the concept of tridimensional momentum thickness. This methodology is evaluated in comparison with the available methods of turbine estimation and with available works on turbine stage tests. It is important to mention that a cascade operating in a turbine stage may receive an unsteady incoming flow due to an upstream cascade, whose effect could impact its performance. This impact is reported to be intimately related to the adopted blade profile [30
]. It is also reported that there is a beneficial effect from ingested wakes in avoiding laminar separation, and thus reducing profile losses in low-pressure turbines [31
]. In fact, the unsteady inflow and the rotor-stator interaction are phenomena much too complex to be predicted on a still immature preliminary design basis.
4.1. Comparison with Traditional Estimation Methods
A comparison of the proposed method with some traditional methods, similar to that done in [32
], is presented in Figure 6
and Figure 7
, in terms of the total enthalpy loss coefficient ξtot
as function of blade aspect ratio h
for typical nozzle and rotor cascades, respectively. The flow angles λ1
are related to the tangential direction. The cascade solidity is considered to be the same for all methods, as given by the Zweifel criterion. Uncompressible flow conditions are assumed, chord Reynolds number is supposed to be 400,000 and trailing edge blockage is 10% in all cases. The following methods are used as references: Soderberg [6
], Anley & Mathieson modified by Dunham and Came [8
], Craig & Cox [10
] and Baljé [11
]. Computational implementation for reference and proposed loss calculation methods were implemented by the author in Matlab 2011b. Traditional estimation models implementation were checked against published results [33
It can be observed that the present work seems to have improved the results of the Baljé [11
] method towards the trusted methods of Ainley and Mattieson modified by Dunham and Came [8
] for the nozzle blades, and Craig and Cox [10
] for rotor blades. The loss sensitivity to cascade solidity is also improved as it is shown to be matched to the level reported in [35
], about 10% increase in loss under ±30% deviation from optimum solidity. The proposed loss model is further validated from experimental results in turbine stages. Complete information on the loss model is presented in [36
4.2. Comparison with Stage Performance Results
] published results of efficiency of extremely low aspect ratio impulse stages tested on air. All the four turbines have the same blade profiles, but different spans. The technique developed by the author [38
] resorts to measuring the torque under an alternative axial outlet rotor, from which the exit nozzle flow tangential momentum is assessed. Although this is a very creative idea, the same degree of reaction was foreseen both for the normal and alternative rotors, which may not be a strictly correct assumption. The impact of this fact may be even more relevant on the stator performance, reason why it was not addressed in this section. The respective aspect ratio h
and total enthalpy loss coefficients ξtot
of the four rotors are shown in Table 2
Good agreement between simulated and experimental results are observed only for rotors a and b. Rotors c and d simulation were not successful, due to the extremely low values of aspect ratio. In these cases the end-wall area is much larger than the profile surface area, so the secondary loss estimation based on profile loss is not suited anymore, limiting the method’s application.
4.3. Design Point Performance Simulation
Some available test results are used in this section to demonstrate the methodology applied to simulate the steady-state design point performance for a turbine stage. A further validation for the proposed loss model is provided from the stage efficiency measurements.
The two tested units are single stage non-condensing steam turbines, partial admission design, applied to oil refinery service. The purpose of this project was to selectively apply this equipment concept to special purpose service, according to the API 612 standard [39
], for which the multi-valve multi-stage design is traditionally specified. The mono-valve single stage units may present a satisfactory performance under favorable conditions of available steam enthalpy drop, speed and output power, with the benefit of a much lower acquisition cost.
The performance tests were carried out at factory test bench, according to ASME PTC6 standard [40
], as a contractual acceptance procedure. The turbine is tested coupled to a hydraulic brake through a reduction gearbox and a torque meter instrumented coupling. The output power and isentropic efficiency are calculated from the orifice plate flow meter and a set of pressure and temperature probes located at the turbine inlet, downstream of the governor valve and exit. The torque measurement is used to check and to validate the thermodynamic analysis results.
Steady-state design point performance simulation of a steam turbine stage is assessed from certain geometric data and service conditions, and also involves real gas behavior. Stage geometry data needed for both stationary and rotating cascades are as follows: number of blades, solidity, aspect ratio, trailing edge blockage, blade flare angle and blade exit angle. Axial and radial clearances are also needed to evaluate leakage losses. Service data are given by the rotational speed, the inlet total pressure and temperature, and the exit static pressure. From the described input data the non-dimensionals specific speed and specific diameter are obtained. A size parameter [41
] must be added in order to give the actual length scale to the non-dimensional geometric parameters.
The problem of simulating a turbine stage performance consists in determining the degree of reaction which provides the better matching of both rotor blade exit angle and arc admission fraction to actual values. Service conditions and geometry data are shown in Table 3
for the two tested units.
The performance simulation results are shown in Table 4
for the two tested units. Some relevant aero-thermal parameters are listed, as well the loss coefficients. Simulated total to static efficiencies are shown to be in agreement with factory test bench measurement results. Estimation of overexpansion losses at supersonic nozzle blade exit flow were done according to Aungier [42
]. Estimation of partial admission losses (filling and emptying loss, scavenge loss and leakage from the active flow to the inactive region) were done according to Baljé [43
The simulated loss breakdown is shown in Table 5
. In fact, commercial steam turbine design is not fully optimized to the specified service due to the utilization of standard-dimension components, like wheels and blades. Despite its advanced rotor blade profile, the detailed analysis clarifies that turbine #2
performance is mainly impaired by leakage losses due to the high nozzle-to-rotor blades axial clearance, suggesting that the wheel was designed for full admission.