4 

Evolution of a centrifugal compressor: From turbocharger to micro gas turbine applications
Fossil fuels are nonrenewable resources which take millions of years to form, and whose reserves are being depleted much faster than new ones are being generated. Furthermore, fossil fuels utilization raises environmental concerns, particularly regarding the global climate change,while the increasing price trend indicates that the fossilfuelsbased energy is becoming a scarce commodity. Therefore, the current energy situation cannot be maintained indefinitely and future energy conversion systems have to be sustainable.
One of the options for a more efficient and sustainable use of fossil fuels as energy sources is arguably distributed generation (DG). Among the various technologies which are currently proposed for DG, micro combined heat and power (microCHP), defined as the process of producing both electricity and usable thermal energy at high efficiency and near the point of use, could play a very relevant role, because it positively integrates technological as well as cultural and institutional components, related to the potential for reducing the ecological impact of electricity conversion.
Micro gas turbines offer many potential advantages in comparison to other conversion technologies suitable for microCHP applications, such as compact size and high specific power; small number of moving parts; low vibrations and noise; low maintenance requirements, which lead to low maintenance costs; high fuel flexibility; possibly short delivery time and very low emissions; modularity; highgrade residual thermal energy.
The main components of a CHP unit based on a micro turbine are the compressor, the turbine, the combustor, the recuperator, the generator, and the heat recovery unit. In the size range of micro gas turbines, radialflow components are usually adopted for the turbomachinery, since they offer minimum surface and endwall losses, and provide the highest efficiency. Centrifugal compressors also provide very high pressure ratio per stage, are less expensive to manufacture, and are similar in terms of design and volume flow rate to those adopted for automotive turbochargers, whose market is currently around two millions units per year, and is therefore characterized by relatively low production costs.
The use of singleshaft radial turbomachinery for micro turbines allows thus for simple designs, with satisfiying aerothermodynamic and economic constraints, thanks to the evolution that automotive turbochargers have experienced in the past seventy years. Furthermore, the introduction of advanced computational fluid dynamics (CFD) tools and of innovative materials in recent years has led to a marked improvement in the current stateoftheart technology of small turbochargers. However, according to some authors, the efficiency levels of centrifugal compressors have almost "stalled" after years of development, while further improvements by means of CFD methodologies would likely to be only incremental.
Nevertheless, improvements in micro turbines performance through suitable modifications of turbocharger technology are to be expected, especially considering that turbochargers usually employ centrifugal compressors with vaneless diffusers in order to maximize the flow range and minimize production costs, wherelse gas turbines require higher efficiency and pressure ratio for a much narrower operating range. Moreover, further engineering challenges are related to the socalled smallscale effects. These are due to i) relatively high viscous losses because of low Reynolds numbers; ii) high relative tip clearance (i.e., the ratio of the tip clearance to the blade height at the impeller outlet) due to manufacturing tolerances; iii) high heat losses, because of large areatovolume ratios; iv) relative large sizeindependent losses, such as those from bearings and auxiliaries, given the low power output.
As a consequence, the main objectives of this work are
1. To develop novel methodologies which allow understanding the flow structure and loss mechanisms of very small centrifugal compressors, and identifying those aspects
whose improvement can lead to higher micro compressor performance.
2. To analyze and quantify the influence of the tip clearance on the performance and flow properties of micro compressors, since the unshrouded impellers used in automotive turbochargers suffer from efficiency decrements, because of the pressure losses and secondary flows caused by very large clearance gaps.
3. To design and build a testrig for the automatic acquisition of the performance maps of very small centrifugal compressors, and for testing either future, new configurations
which aim to improve the performance of an exemplary micro turbine compressor, or other very small centrifugal compressors.
4. To develop an original optimization methodology for turbomachinery components, to be further utilized for the improvement of the performance of an exemplary micro turbine compressor, through the investigation of vaned diffusers, which are claimed to exhibit higher static pressure recovery and efficiency than vaneless diffusers, at the expenses of a narrower operating range.
In this study, the recuperated micro gas turbine developed by the Dutch company Micro Turbine Technology B.V. (MTT) has been utilized as an illustrative example. The MTT micro turbine delivers electrical and thermal power output up to 3 and 14 kW, respectively, and will be primarily applied in microCHP units for domestic dwellings. The turbomachinery consists of a commercial offtheshelf automotive turbocharger, made of a centrifugal compressor, a radial turbine, and oillubricated bearings. A cycle study of the MTT recuperated micro gas turbine has been carried out in order to assess the impact of the centrifugal compressor performance on the system performance. The analysis proved that increasing the performance of the centrifugal compressor adopted for the MTT micro turbine is pivotal in order to achieve higher performance levels of the microCHP system.
The main conclusions of the work presented here are summarized as follows:
1. A fully automated optimization methodology has been developed by integrating an optimization algorithm, a geometry generator, a grid generator, a CFD solver, and a post processor. This methodology can be used for the optimization of turbomachinery components, but has been applied here to the design and optimization of vaned diffusers for the exemplarymicro compressor. The optimized vaned diffusers led to increased static pressure recovery, but the compressor efficiency was lower than that of the vaneless configuration, because of larger total pressure losses.
2. The testrig, which has been designed and built for the automatic acquisition of the performancemaps of very small, highspeed centrifugal compressors, proved to be robust, reliable, and versatile. An experimental campaign has been carried out in order to quantify the aerodynamic performance of the exemplary compressor, and the test data, summarized in the form of performance maps and tables, have been used to validate the results of the numerical analyses shown in this dissertation. Furthermore, the testrig will be a useful tool in the development of future, new designs which aim at improving the performance of the exemplary micro turbine compressor, and will be utilized to test other very small centrifugal compressors for a variety of different applications.
3. A new onedimensional (1D) method for the assessment of the performance (i.e., stage totaltototal pressure ratio and isentropic efficiency; impeller inlet and outlet velocity triangles; impeller internal, external, and mixing losses; vaneless diffuser losses; volute losses) of very small centrifugal compressors has been developed on the basis of two very wellknown design methodologies, namely the single and twozone model. This novel tool combines the advantages of the two, since it distinguishes between high and lowmomentum flows within the impeller bladed passages as possible with the twozone model, and allows evaluating the impeller loss mechanisms, as possible with the singlezone model.
This dissertation is structured as follows. Chapter 1 illustrates the concept, potential, and technology of microCHP within the framework of different energy scenarios. The motivation
and scope of this work, and the outline of the dissertation are also given here.
Chapter 2 presents the new 1D method for the assessment of the performance and loss mechanisms of very small centrifugal compressors. The novel methodology has been applied here to the exemplary micro centrifugal compressor. The numerical results computed by this tool have been validated against the experimental results obtained with the testrig. The comparison has been performed at 190 and 220 krpm, and varying mass flow rate, respectively, and shows a good agreement, since the model is able to capture the pressure ratio and efficiency trends. However, in proximity of the choking condition the difference between the numerical and test data is higher. Furthermore, at the micro turbine design point (i.e., mass flow rate equal to 50 g/s and rotational speed equal to 240 krpm), the model overpredicts the pressure ratio, but underpredicts the efficiency. At the micro turbine design point, it has been calculated that the skin friction losses contribute to the largest efficiency decrease, followed by the mixing
losses, and the vaneless diffuser losses.
Chapter 3 describes the experimental setup which has been designed and built for the acquisition of the performance maps of very small, highspeed centrifugal compressors. The compressor impeller is driven by a turbine powered by pressurized air coming from a buffer tank, pressurized in turn by two screw compressors. The shaft speed is varied by a turbine control valve, while further equipment necessary to operate the testrig was also integrated into the setup, as well as the instrumentation and data acquisition system. The testrig can currently accomodate impellers with diameters up to 20 mm, and rotational speeds up to 220 krpm. However, rotational speeds up to 240 krpm (i.e., the micro turbine design point) are deemed within reach with suitable improvements of the compressor testrig. The uncertainty propagation analysis has also been performed. The results show that for the exemplary micro compressor the static pressure uncertainty highly influences both the pressure ratio and efficiency
uncertainties. In particular, the uncertainty of the compressor inlet static pressure is preponderant with respect to that of the outlet static pressure. Substituting the actual pressure transmitters with ones having better accuracy and lower full scale would therefore reduce the uncertainties of the final results. On the contrary, the total temperature uncertainty contributes to the efficiency uncertainty to a lower degree, while the mass flow rate uncertainty does not have any impact at all on the uncertainties of the final results.
Chapter 4 shows the numerical study performed with a commercial CFD code which solves the threedimensional (3D) Reynolds averaged NavierStokes (RANS) equations. Steadystate simulations of the exemplary centrifugal compressor have been carried out to approximate the real, timedependent flow physics with satisfactory results and shorter computational time with respect to an unsteady approach. The results of the numerical analysis, which has been performed at the micro turbine design point, show that the flow separates due to the supersonic relative Mach number at the impeller blades tip. Subsequently, a lowvelocity region develops on the blades suction side, enlarges along the streamwise direction, and leads to the generation of high losses in proximity of the impeller outlet, at the shroud. Furthermore, the calculated static pressure recovery coefficient of the vaneless diffuser of the exemplary compressor stage is equal to 0.4. It is thus located at the lower end of the ranges documented in the
literature. Finally, it has been calculated that for every 1%increase of the impeller tip clearance, the stage totaltototal pressure ratio and isentropic efficiency decrease by 1.3%and 0.6%, respectively. The impeller efficiency drop due to the impeller tip clearance is two times larger than the loss documented in the literature for larger centrifugal impellers.
Chapter 5 describes the influence of the diffuser on the compressor performance. Firstly, an overview of the impeller outlet flow phenomena is given, in order to identify their effects on the downstream flow field. A brief description of the two main categories of diffusers (i.e., vaneless and vaned) follows. Finally, the most important design parameters of a vaned diffuser are highlighted.
Chapter 6 illustrates the developed optimization methodology. Firstly, the optimization of vaned diffusers has been performed by coupling a genetic algorithm (GA) to a inhouse twodimensional Euler CFD code, in order to test this optimization strategy. Secondly, the GA has been coupled to a commercial 3D RANS CFD code, in order to account for the viscous effects and the impellerdiffuser interaction. In this case, the GA has been assisted by a Kriging metamodel, in order to reduce the computational costs, while a multiobjective problem has been solved by minimizing, separately and simultaneously, a function of the stage totaltostatic pressure ratio, and a function of the stage totaltototal isentropic efficiency. The relative position of the vanes between the diffuser inlet and outlet, their inclination with respect to the radial direction at the leading and trailing edges, the diffuser outlet radius, and the vane number have been selected as design variables. At first, the optimization methodology has
been utilized to design vaned diffusers for the exemplary compressor, at the micro turbine design point. In this case, the efficiency of the simulated most efficient optimized vaned diffuser is 1.9% lower than that of the vaneless diffuser. The vaned diffuser however exhibits a 7.4%higher static pressure recovery. Subsequently, a larger impeller diameter, which delivers a higher pressure ratio at the same rotational speed, has been considered. At the micro turbine design point, the efficiency and static pressure recovery of the simulated most efficient optimized vaned diffuser are respectively 1.8% and 16.6% higher than those of the vaneless configuration. As a consequence, the use of vaned diffusers with a lowpressure pressure ratio compressor is beneficial only in terms of static pressure recovery, while a reduction of the friction losses, leading to increased efficiencies, can be achieved only in the case of high dinamic heads available at the diffuser inlet, due to larger impellers.
Chapter 7 draws the conclusions regarding the work presented in this dissertation, while recommendations are suggested for future research activities.

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5 

Smart Operation of Gas Turbine Combined Cycle Plants: Prediction and Improvement of Thermal Efficiency at Part Load
This thesis investigates various operational aspects of Gas Turbine Combined Cycle Power Plants (GTCC). GTCC power plants are expected to play an increasingly important role in the balancing of supply and demand in the electricity grid. Although originally meant for predominantly base load operation with high efficiencies, market circumstances, namely the increasing supply of unpredictable wind and solar power, force these units to be operated frequently across a wide range of load settings.
The required flexibility opens a need for models, that can predict the plant performance accurately at design point as well as offdesign conditions. The models and performance data, made available by equipment manufacturers, are usually too general to be applied for accurate prediction and optimization purposes. Adding to this, the electricity producing companies usually do not possess detailed design information, so that creating accurate process models presents an extra challenge.
The chapters of this thesis are dedicated to the proposal of several methods for overcoming challenges related to the operation of existing gas turbine combined cycle plants in current and future energy markets. All models and procedures developed in the framework of this thesis, are applied to the Alstom KA261 GTCC as a case study. Two of these units were installed at the Maxima Power Station in Lelystad for GDF SUEZ Energy The Netherlands.
The current study is first placed in the broader context of the developments in the electricity market, and of research fields related to this subject. The importance of accurate simulation tools is motivated, and the potential role of uncertainty management and optimization is put forward. The implications of the market developments are synthesized into a concise problem statement.
The productive core of GTCC plants is the gas turbine, especially when there is no external firing in the steam cycle. A step wise method for accurately modeling the design and offdesign steady state performance of gas turbines is presented. Tuning performance models to measured data typically available to an engine user is an important task. Therefore, a method for achieving this is proposed and applied to a case study: the GT26, an industrial gas turbine (part of the KA26 plant) with two sequential combustor components. The results of this modeling effort indicate that the accuracy decreases towards part load.
Thermodynamic modeling of the steam cycle, although a widely practiced discipline, still presents some challenges in case of industrialsize units. Secondlaw analysis is often added to thermodynamic flow sheet calculations; this can be enhanced by analyzing the interaction between plant components with the help of a novel procedure presented in the thesis. For this purpose, the plant model is calculated over a randomly and uniformly distributed set of input conditions, calculating the (second law) thermodynamic losses of major components for every case. (The term numerical experiment is used for this procedure.) After this, the resulting data is processed and visualized to reveal expected as well as unexpected mutual relations between the losses of individual plant components.
When gas turbine and steam cycle models, and computer models in general, are applied to make predictions, and economical decisions are based on these models, there is always an amount of uncertainty present with respect to the validity of the predictions. Quantification and reduction of this uncertainty can be of significant value for stakeholders.
In this context, an existing method for statistical analysis and calibration of computer models, the Kennedy & O'Hagan framework, is applied to the the previously presented gas turbine and steam cycle models. The purpose is to enhance the accuracy of (especially) part load efficiency prediction by calibrating the models with the available (industrial) measurements.
The mathematical tools applied in this framework are explained, along with the manner in which it is applied to the gas turbine and steam cycle models respectively. For plant performance prediction, it is necessary to integrate the models, so that uncertainties in one model are propagated through the next. Two methods are described for achieving this: integration of the models can be done either before or after calibration. The two stochastic integration methods are applied to predict the efficiency of the case study plant. While both methods produce accurate results, there is an indication that integration after calibration is slightly more accurate.
The most important objective for the current study, besides accurate performance prediction, is the proposal of efficiency optimization methods. The final part of the thesis illustrates methods for analyzing efficiency improvement possibilities of existing (gas turbine combined cycle) power plants, and optimizing part load efficiency with steady state plant models.
Firstly, the data from the numerical experiment mentioned earlier are processed. By comparing how strong the exergy losses in major components are correlated to overall thermal efficiency of the plant, the low pressure steam turbine is shown to be the component whose thermodynamic losses have the largest effect on the variations in overall plant efficiency. However, it is also known that gas turbine losses represent the largest exergy loss. This seeming contradiction is thoroughly explained in the thesis.
By using a clustering algorithm, operational regimes are revealed with respect to the losses in the low pressure steam turbine and gas turbine. Efficiency optimization is performed at ambient conditions corresponding to these distinct operational regimes. The results of optimization indicate that the optimum set of operational settings is different for each of the identified regimes, thereby confirming that they are distinct regimes.
After using deterministic models for the efficiency maximization, model uncertainty is incorporated in the calculations, and the stochastic models presented earlier are applied. The difference with the previous optimizations is that in this case, the applied model has been proven to give more accurate results, and it provides the statistical distribution and expected value of the plant efficiency, not just a deterministic value. The results of optimization under uncertainty are compared to results of deterministic optimization under equal ambient conditions: the resulting optimal operational settings for both cases are shown to be similar in many aspects; differences are analyzed and put into perspective.
The final part of the thesis synthesizes the main conclusions and recommendations from the previous substudies and places them in the general context of the research field. Suggestions are proposed for possible applications of the proposed methodologies to problems which are outside the scope of the thesis.

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