Today an increasing need for gas turbines with extremely low flow rates can be noticed in many industrial sectors, e.g. power generation, aircraft or automotive turbo chargers. For any application it is essential for the turbine to operate at best possible efficiency. It is known that for turbines the specific optimum achievable power output decreases with smaller size. A major contribution for this reduction in efficiency comes from the relative increase of aerodynamic losses in smaller turbine stages. In the early turbine design stage, easy and fast to use two-dimensional calculation codes are widely used. In order to produce qualitatively good results, all of these codes contain a diversity of loss models that more or less exactly describe physical effects which generate losses. It emerges to be a real problem that most of these empirical models were derived for rather large scale turbo machines and that they are not necessarily suitable for application to small turbines. In this paper many of the commonly known and well established loss models used for the preliminary design of radial turbines were collected, reviewed, and validated with respect to their applicability to small-size turbines, i.e. turbines of inlet diameter smaller than 40 mm. Comprehensive numerical investigations were performed and the results were used to check and verify the outcome of loss models. Based on the results, loss models have been improved. Furthermore, new correlations were developed in order to raise the quality of loss prediction especially for the design of small-size turbines. After receiving an optimum set of loss prediction models, all of them were implemented into a two-dimensional solver program for the analytical iterative solution of a complete turbine stage. Hence a powerful tool for preliminary radial turbine design has been created. This program enables the user to analytically evaluate the effects of changing key design properties on performance. These are amongst others the optimum rotor inlet flow angle according to the slip-factor definition, the value of flow deviation, and hence the optimum blade outlet angle for a minimum adverse flow-swirl at turbine outlet. Complementarily the turbine key performance indicators, e.g. pressure ratio, power output, rotational turbine speed, and mass flow can be calculated for optimum efficiency of a given turbine geometry. The paper presents the most important loss models implemented in the new code and weights their relative importance to the performance of small size radial turbines. The data acquisition was done using the new code itself as well as accompanying full 3D CFD calculations.

Designing turbine wheels for automotive turbochargers one is faced with a multidisciplinary design problem with many input and output parameters. Especially in the automotive industry short development cycles for high quality products in a competitive environment are daily routine. For meeting these requirements optimization algorithms can be a powerful tool in the design process. This paper presents the multidisciplinary optimization of an automotive mixed flow turbine wheel used in a 4 cylinder 1.6 l spark ignition engine. Before describing the optimization workflow in detail, the requirements for turbines operating in an automotive environment under pulsating flow conditions and during an engine load step are discussed. From there objectives for a multidisciplinary optimization are derived. The turbine wheel is optimized with respect to maximizing efficiency in two design points and minimizing its moment of inertia. For the optimization process, an algorithm based on evolution theory is used. As constraints, the operating points are fixed and the natural frequencies are limited to ensure the mechanical strength of the turbine. To speed up the optimization process meta models based on neural networks are applied. Three designs of the Pareto frontier are chosen and their characteristics are discussed. Using statistical methods, the interaction of the input variables and their impact on turbine performance are presented.

This paper presents a study on the influence of the degree of reaction (DoR) on turbine performance under highly pulsating inflow. A reference test turbine wheel is designed and scaled to three different wheel diameters while an identical flow capacity of all three turbines is provided by adjusting the volute size. Hence, the three turbines differ by their DoR, inertia and efficiency characteristic. The investigation is done completely numerically using highly validated models. Naturally, the pulsating flow character of a 4-cylinder gasoline engine requires unsteady CFD. In addition steady-state turbine maps were calculated beforehand as a reference base. The results of the steady state calculation show that for the combination of the bigger turbine wheel with the smaller turbine volute the peak efficiency is smaller but is shifted towards higher pressure ratios respectively to lower blade speed ratios. This is fundamentally beneficial for turbines in automotive turbochargers for gasoline engines characterized by highly pulsating flow conditions, in particular at lower engine speeds. For the transient flow calculations with pulsating turbine inflow, the hysteresis loop and the turbine power generation was investigated. It is shown that the smallest volute compared to the biggest one causes a more contracted hysteresis loop combined with increased power output within one pulse cycle. In order to include the influence of moment of inertia, the turbines with varying DoR but same flow capacity were analytically compared with a 1D code simulating engine load step operation. Thus, the paper shows the effect of turbine DoR on both, steady-state turbine performance under pulsating inflow and the capability for optimum engine load step operation.

A method for evaluating the transient performance of a turbocharger (TC) is so-called load step tests. In these tests, the load of the engine is increased at constant engine speed and the time measured from the start to the end of the load step is measured. Usually, these tests can be run relatively late in the development process, since hardware needs to be already available. In order to judge the transient TC performance at an earlier stage, engine process simulations are run using maps of compressor and turbine. For the turbine, these maps usually need to be extrapolated, since only a certain range of each speed line can be measured on a standard gas stand. Furthermore, because of the exhaust gas pulsation of the engine, it is known that the turbine performance differs from the steady-state case which the maps rely on. This has to be respected by additional models. Using computational fluid dynamics (CFD) simulations, the transient performance of the turbine can be analyzed independent from steady-state maps. So far, these investigations have been usually performed with a constant turbine speed. In this paper, a method is presented which includes the speed fluctuations of the TC caused by the exhaust pulsations as well as the change in mean speed during the load step by including compressor and engine in the CFD analysis with User-Fortran models. Results for a load step from 21,000 rpm to 196,400 rpm are discussed.

With an increasing need for gas turbines with rather low flow rates in many industrial applications, e.g. decentralized power generation, aircrafts or automotive turbochargers, the development of small size radial turbines becomes more and more important. A major step in the development of a radial turbine stage is the preliminary design, which is the definition of basic geometrical features and the calculation of general turbine flow parameters at the design point and within the operating range. These are mainly the rotational speed, the expansion ratio, the flow rate and in particular the expected turbine efficiency. In a radial turbine stage, the volute component delivers the flow to the rotor wheel and according to the geometrical form it defines major flow parameters like the mass flow parameter or the absolute rotor inlet flow angle. Amongst others, the way the flow enters the turbine wheel represents one of the most important loss generating factors. Thus, on the one hand an approach is necessary for the calculation of the optimum rotor inlet flow angle, in order to avoid dispensable losses due to secondary flow in the turbine wheel region. On the other hand, the volute tongue generates flow non-uniformity which has an effect on the overall circumferential averaged rotor inlet flow angle. Furthermore, the local flow pattern downstream of the volute tongue can generate suboptimal flow conditions for the turbine wheel. Hussain and Bhinder [1] measured the flow field at the outlet of a vaneless volute at different circumferential positions and detected a variation of the outlet angle of about Δα = 10°. The authors conclusion was, that the influence on the stage performance of flow non-uniformity generated by the volute could exceed the one of pressure losses through the volute. In this paper, the effect of different geometrical volute parameters on the flow condition especially at the turbine wheel inlet area is investigated. Experimental data of the influence of different volute tongue geometries on the flow field is difficult to generate. Hence, comprehensive numerical investigations are made using steady 3D-CFD calculations of the turbine volute as well as calculations of complete turbine stages including a turbine wheel geometry. Based on the numerical results, a design guideline is developed to estimate the influence of the geometric volute parameters on the flow and to raise the quality of the preliminary design process.

As the pursuit of improved aerodynamic performance on turbochargers continues to push the boundaries of mechanical design, the risk of high cycle fatigue (HCF) failures of turbine wheels is elevated and drives the need for improved methods of analytical predication. Turbine wheel HCF is caused by the asymmetrical aerodynamic loading associated with the application of variable geometry turbines and compromised inlet/outlet geometries that accommodate packaging turbochargers in engine compartments. Historically, the turbocharger industry has focused on blade pass as the primary cause of HCF. BorgWarner presents an analytical technique to limit the risk of HCF by calculating all critical orders that intersect blade natural frequencies and quantify the relative energy of each forced excitation frequency. The geometry of a turbine volute mainly determines the inflow angle into the turbine wheel. Thus, for the thermodynamically optimized turbine a variable inflow angle dependent on the engine operating point is desirable. The Variable Turbine Geometry (VTG) concept applies adjustable turbine inlet guide vanes to approach the ideal velocity triangle. One of the inevitable disadvantages associated with either fixed or variable turbine nozzle vanes is the generation of wakes and pressure fluctuations upstream of the turbine wheel inducer. The resulting circumferentially non-uniform flow conditions apply a transient load on the rotating turbine wheel. Due to complexity of the VTG design including non-uniformly spaced vanes and struts, the excitation sources and resulting excitation orders are not readily apparent. The analytical method described in this paper applies a transient 3D Computational Fluid Dynamics (CFD) model of the rotor-stator interaction to calculate the time-dependent pressure fluctuations experienced by the turbine wheel blade. This data is used to extract the forced excitation function at the turbine wheel. Finite Element (FE) analysis is applied to determine the mean and dynamic stress. In case of dynamic stress, system vibration modes and the influence of local harmonic excitation on blade stress amplitudes is analyzed. The fixed-speed FE results are scaled for the effect of flow and speed by use of empirical data from strain-gauge measurement. Hence, computational methods combined with experience from experimental measurements are used to determine critical rotational speeds for a given turbocharger geometry. This method allows the analyst to predict the highest energy excitation orders and reduce the risk of turbine wheel fatigue damage. Since the durability of a turbine wheel cannot yet satisfactorily be quantified by the described computational method, the analysis results are used as rotational speed input in subsequent durability tests in order to reduce the necessary amount of testing resources.

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B o rg W a rn e r T u rb o S ystem s E n g in e e rin g G m bH , M a rn h e im e r StraBe 8 5 /8 7 , K irc h h e im b o la n d e n 6 7 2 9 2 , G erm any e -m a il: m g u g a u @ b o rg w a rn e r.c o m Harald Roclawski D ep a rtm e n t o f M e cha n ical E n g in e erin g, In s titu te o f F lu id M e cha n ics and T u rb o m a c h in e ry ,