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.
A computational study was performed for the flow and heat transfer in rotating coolant passages with two legs connected with a U-bend. The dimensionless flow conditions and the rotational speed were typical of those in the internal cooling passages of turbine blades. The calculations were performed for two geometries and flow conditions for which experimental heat transfer data were obtained under the NASA HOST project. The first model had smooth surfaces on all walls. The second model had opposing ribs staggered and angled at 45 deg. to the main flow direction on two walls of the legs, corresponding to the coolant passage surfaces adjacent to the pressure and suction surfaces of a turbine airfoil. Results from these calculations were compared with the previous measurements as well as with previous calculations for the nonrotating models at a Reynolds number of 25,000 and a rotation number of 0.24. At these conditions, the predicted heat transfer is known to be strongly influenced by the turbulence and wall models. The differential Reynolds-stress model (RSM) was used for the calculation. Local heat transfer results are presented as well as results averaged over wall segments. The averaged heat transfer predictions were close to the experimental results in the first leg of the channel, while the heat transfer in the second leg was overestimated by RSM. The flow field results showed a large amount of secondary flow in the channels with rotational velocities as large as 90 percent of the mean value. These secondary flows were attributed to the buoyancy effects, the Coriolis forces, the curvature of the bend and the orientation of the skewed ribs. Details of the flow field are discussed. Both the magnitude and the change of the heat transfer were captured well with the calculations for the rotating cases.
A computational study was performed for the flow and heat transfer in coolant passages with two legs connected with a Ubend and with dimensionless flow conditions typical of those in the internal cooling passages of turbine blades. The first model had smooth surfaces on all walls. The second model had opposing ribs staggered and angled at 45 0 to the main flow direction on two walls of the legs, corresponding to the coolant passage surfaces adjacent to the pressure and suction surfaces of a turbine airfoil. For the ribbed model, the ratio of rib height to duct hydraulic diameter equaled 0.1, and the ratio of rib spacing to rib height equaled 10. Comparisons of calculations with previous measurements are made for a Reynolds number of 25,000. With these conditions, the predicted heat transfer is known to be strongly influenced by the turbulence and wall models. The k-e model, the low Reynolds number RNG k-e and the differential Reynolds-stress model (RSM) were used for the smooth wall model calculation. Based on the results with the smooth walls, the calculations for the ribbed walls were performed using the RSM and k-e turbulence models. The high secondary flow induced by the ribs leads to an increased heat transfer in both legs. However, the heat transfer was nearly unchanged between the smooth wall model and the ribbed model within the bend region. The agreement between the predicted segment -averaged and previously -measured Nusselt numbers was good for both cases.
In the present study, the entire energy balance of a turbocharger is investigated applying an experimentally validated numerical approach with the intention of examining the heat transfer mechanism inside the turbo. The heat transfer results thus obtained are used amongst others to determine the diabatic effects on the turbine and compressor flow resulting in heat-transfer corrected performance maps. These maps are applied as matching data to 1D engine performance calculation and are utilized in the engine process simulation procedure with GT Power™. In detail, the numerical approach of the entire energy balance is based on a thermal network model (RC-resistance / capacity) where the 3D geometry of the turbocharger is subdivided into segments. These segments are defined as lumped mass elements of the thermal network. The entire energy balance of the modeled turbo is fulfilled by coupling the thermal network of the structure to the enthalpy flows of the turbine, compressor, oil circuit, and water coolant as well as the heat losses to ambient. The heat transfer between the structure and the enthalpy flows, respectively, is achieved by using heat transfer coefficients (HTC) performed in accordance with Nusselt-No. laws. Heat loss to ambient is expressed by natural convection and radiation. In general it would be possible to perform the energy balance of the turbo model in the steady state or transient regime. A time-governed finite volume calculation scheme is used for the solution algorithms. The code of the turbo heat transfer approach (THT) is written in Matlab™, something which facilitates flexible adjustments on the algorithm and good post-processing capabilities. Two routes are resorted to for validating the THT approach. Gas stand tests with instrumented turbochargers using thermocouples and pressure sensors are conducted in the first assignment for generating the essential experimental data. Segmentation of the 3D turbocharger geometry into discrete elements is accomplished in the second assignment by means of CAD technology and used for both, the setup of the THT thermal network model and in parallel for the generation of an AnsysCFX™ 3D CAE model. The same HTC thermal boundary conditions are applied to both models which is favorable in as far as it provides a one-to-one comparison of the heat flux and mean temperature in each segment of the two models, Matlab™ THT and CFX™. Ansys™ model heat flux and mean segment temperature results are validated by the measured experimental temperature data. The THT network model properties such as segment volume, areas, volume, and element distances are calibrated applying the results of the 3D CAD and CAE Ansys™ model. The results of the two numerical models are compared with each other, thus demonstrating the qualitative and quantitative level of agreement. The THT approach that has been developed is successfully applied to GT Power™ gasoline engine model. A thermal network model of that applied turbocharger was setup and validated by gas-stand and engine data obtained on an experimental basis with an instrumented turbo. Finally it was possible to demonstrate that the heat-transfer corrected turbocharger performance map data which was provided utilizing the THT model approach brings about a significant benefit to the determination process aimed at achieving a tailored turbocharger thermodynamic layout.
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