Equation-oriented methods for design optimization and performance analysis of radial inflow turbines

This work will present a model for the preliminary optimized design of a radial turbine and an analysis of the most relevant loss models for efficiency prediction.A one-dimensional code, Radial Turbine Global Design, was developed in MATLAB environment. The model developed has the objective to estimate the efficiency and optimization of the parameters related to it, and losses prediction.The flow that through a turbine is complex and many mechanisms of the flow losses in turbine, have not be known well. The computational fluid dynamics CFD simulations is based on complex three-dimensional viscous methods, which require considerable iterations and, therefore time, in order to obtain an improvement of the geometry, through the convergence to an acceptable solution often not optimal. While, can be used of one-dimensional models able to predict the global design of the machine based on the combination of empirical and experimental loss models, able to provide a good performance estimate with reduced times. In this work, the loss models are analyzed and developed to obtain useful thermodynamic and geometrical information, necessary for an optimization CFD simulation.The RTGD has proven useful for the geometric design three-dimensional of the rotor blades and was tested by considering literature data of real radial turbines that use both Aria and Argon as working fluid, in addition it was compared with the NASA code RIFTUD.The code has excellent reliability because the results obtained reproduce the turbine geometry with a low error compared to the literatures case.Furthermore, RTGD can predict turbine performance through two approaches, the first considering the turbine geometry and the second considering the enthalpy drop due to losses. The second approach for estimating efficiency is necessary in order to confirm the one calculated with the first approach, and therefore the good geometric design of the turbine.The code, after being validated, was used for the radial turbines design for space applications for expander cycle rocket engines which require a high efficiency and a low expansion ratio.

A methodology for the preliminary design and performance prediction of high-pressure ratio radial-inflow turbines

A comprehensive one-dimensional meanline design approach for radial inflow turbines is described in the present work. An original code was developed in Python that takes a novel approach to the automatic selection of feasible machines based on pre-defined performance or geometry characteristics for a given application. It comprises a brute-force search algorithm that traverses the entire search space based on key non-dimensional parameters and rotational speed. In this study, an in-depth analysis and subsequent implementation of relevant loss models as well as selection criteria for radial inflow turbines is addressed. Comparison with previously published designs, as well as other available codes, showed good agreement. Sample (real and theoretical) test cases were trialed and results showed good agreement when compared to other available codes. The presented approach was found to be valid and the model was found to be a useful tool with regards to the preliminary design and performance estimation of radial inflow turbines, enabling its integration with other thermodynamic cycle analysis and three-dimensional blade design codes.

Radial turbines’ preliminary designs are usually carried out through some dimensionless approaches, such as the loading-to-flow-diagram and/or the blade speed ratio. In case of variable nozzle radial turbines, multi-points specifications must be considered, related to the improvement of the operating range. As preliminary design correlations and standards usually taken into consideration arise from studies dedicated to fixed geometry radial turbines, they need to be updated with regard to nozzle off-design opening configurations. This paper provides some theoretical basics in order to help designers considering variable geometry problems. Some complementary elements about the dimensionless methods are given by taking into account the nozzle opening effect. Then, useful considerations are brought regarding the preliminary design of variable geometry radial turbines with multi-points specifications.

Microturbines have been developed as an important power unit for distributed generation (DG) or distributed energy resource (DER) options [1]. They have been established and are widely used in aircraft and power applications, due to their easy installation, reliability, high performance, multi-fuel capabilities and low emission [2]. However, the aerothermodynamic design of a radial turbine still poses a challenge due to its high rotational speed and high inlet temperature, which influence the centrifugal stress and the rotor structural integrity. This paper presents the numerical investigations on the aerothermodynamic design of the nozzle and the radial inflow rotor for a 600 kW simple cycle gas turbine engine using a One-dimensional Computer FORTRAN Code (OFC) [3], on the grounds of non-dimensional parameters aimed at computational and work time reduction. This program utilizes a one-dimensional solution of flow conditions through the turbine along the meanline. The referred computer program is an effective performance prediction tool mostly in the initial stage of the preliminary design and can be used to quickly investigate and calculate the number of design options prior to any details of the vane and blade geometry. In order to find the most promising design option, a computational fluid dynamics (CFD) simulation has been used to study the performance, the aerothermodynamic design and the flow characteristics of the turbine components. The OFC results were compared with the CFD simulation, a computer program for the design analysis of radial inflow turbines, and analytical results taken from specialized literature showed the results were in agreement.

The use of supercritical fluids has been identified as potential solution in realizing highly efficient and compact sized power systems. In this study, the effect of design power scale and specific speed on supercritical CO2 operated radial inflow turbines within the power range of 0.1 MW–3.5 MW is investigated and analyzed. A radial turbine design tool including loss distribution analysis based on loss correlations was developed. In general, the SCO2 radial turbines can be designed to have high efficiency with efficiency ranging from over 80%–87% depending on the turbine design power scale. On the other hand, the turbine dimensions are small and the required rotational speeds are significantly high even at MW scale designs. It was observed that the specific speed and mass flow rate highly affect both the geometry and the turbine loss distribution. Turbine designs with highest isentropic efficiencies were observed with specific speeds ranging from 0.50 to 0.60. With the lowest investigated turbine power outputs from 100 kW to few hundreds of kW the tip clearance loss is the most significant loss whereas the passage, stator and exit kinetic loss are the most significant loss sources at higher power levels.

: Small radial inflow turbines have various applications in industry and are successfully being used as a major component of gas turbines and turbochargers. The performance of the turbine is of great importance for the success of these systems. Although the design of radial inflow turbines has improved in the last few years, the detailed aerodynamic study of these components still needs considerable attention. Better understanding of the flow processes involved in these machines will provide a good basis for the design of improved components and for this purpose a joint research programme has been undertaken by Cranfield, the US Army Research Office and Turbomach (San Diego). The main objective of the study was to investigate the flow processes involved in the radial inflow turbine using experimental methods. The work presented in this report describes the various steps undertaken to perform these studies together with results. The project involved two phases, the first measurements downstream of the rotor and the second measurements between the nozzle guide vanes and rotor inlet. The scope of the study was limited to two man years during which considerable success was achieved in obtaining the desired measurement but more time to further reduce this data and to compare with computational results, which was outside the scope of the present study, would have been advantageous. The studies using laser anemometry undertaken downstream of the turbine rotor indicated a swirling flow with a region of counter-rotating flow in the centre. A cobra probe was used to compare with the laser anemometry results. Both measuring techniques show similar trends of flow velocity and flow angle at various running conditions.... Radial Turbines, Laser Anemometry.

The blades of turbocharger impellers are exposed to unsteady aerodynamic forces, which cause blade vibrations and may lead to failures. An indispensable requirement for a safe design of radial inflow turbines is a detailed knowledge of the exciting forces. Up to now, only few investigations relating to unsteady aerodynamic forces in radial turbines were presented. To give a detailed insight into the complex phenomena, a comprehensive research project was initiated at the Institut für Thermische Strömungsmaschinen, at the University of Karlsruhe. A turbocharger test rig was installed in the high pressure, high temperature laboratory of the institute. The present paper gives a description of the test rig design and the measuring techniques. The flow field in a vaneless radial inflow turbine was analyzed using laser Doppler anemometry. First results of unsteady flow field investigations in the turbine scroll and unsteady phase resolved measurements of the flow field in the turbine rotor will be discussed. Moreover, results from finite element calculations analyzing frequencies and mode shapes are presented. As vibrations in turbines of turbochargers are assumed to be predominantly excited by unsteady aerodynamic forces, a method to predict the actual transient flow in a radial turbine utilizing the commercial Navier Stokes solver TASCflow3d was developed. Results of the unsteady calculations are presented and comparisons with the measured unsteady flow field are made. As a major result, the excitation effect of the tongue region in a vaneless radial inflow turbine can be demonstrated.

Preliminary design, optimization and CFD analysis of an organic rankine cycle radial turbine rotor

Preliminary design and CFD analysis of a radial inflow turbine and the turbine seal for an organic Rankine cycle using zeotropic mixture

This introductory Chapter is a synthesis of the text titled “Lecture notes on Fluid Machines—Gambini and Vellini” (in Italian), 2007, adopted for the Tur-bomachinery and Energy Systems courses for students of the bachelor’s Degree in Mechanical and Energy Engineering of the University of Rome Tor Vergata. This Chapter intends to provide a summary of the basic principles of thermodynamics and fluid-dynamics applied to turbomachinery in order to define all the performance parameters (work transfer, isentropic and polytropic efficiency, nozzles and diffusers efficiency, degree of reaction, etc.) used in the proposed procedures for turbomachinery selection and preliminary design (Chaps. 2– 7). After introducing the basics of the First and Second Principles of Thermodynamics (Sect. 1.1), the energy equation is deduced in the mechanical and thermodynamic form (Sect. 1.2). Then, fluid properties are introduced (Sect. 1.3). Next, we analyze work transfer in turbomachines handling compressible (Sect. 1.4) and incompressible (Sect. 1.5) fluids, and we define isentropic, polytropic (Sect. 1.4), and hydraulic efficiency (Sect. 1.5). Then, the fluid flow in turbomachinery is studied through cardinal equations, and the Euler equation is deduced (Sect. 1.6). The principles of turbomachinery operation are therefore illustrated, highlighting stator and rotor configurations and the relative energy transfer processes (Sect. 1.7). Afterwards, an energy analysis of both axial and radial turbine and compressor stages is carried out (Sect. 1.8), aimed at defining all the performance parameters (work transfer, efficiency, degree of reaction, power, etc.). Finally (Sect. 1.9), we analyze losses in turbomachinery stages by highlighting the loss sources and providing a classification of these losses for both axial and radial stages. Throughout the discussion, real fluids are considered, illustrating only a few particular applications for perfect gases.

The radial turbine is a key component of the Organic Rankine Cycle (ORC) power generation system. In order to improve the performance of ORC system for low temperature heat sources, a 150kW radial turbine using R600a has been designed and analyzed. First, the aerodynamic calculation of the radial turbine was conducted and one-dimensional aerodynamic parameters were obtained. Then three-dimensional CFD numerical analysis has been conducted to optimize the geometric design of the radial turbine. The results show the distribution of the flow field around the blades at different height and streamline distribution from leading edge to the trailing edge. At last, the effect of rotation speed on the performance of radial turbine was analyzed. The results can provide basic data for the design of radial turbine of ORC power generation system for low temperature heat sources.

The present study describes the application of a preliminary design approach for the optimization of an organic Rankine cycle radial turbine. Losses in the nozzle the rotor have initially been modelled using a mean-line design approach. The work focuses on a typical small-scale application of 50 kW, and two working fluids, R245fa (1,1,1,3,3,-pentafluoropropane) and R236fa (1,1,1,3,3,3-hexafluoropropane) are considered for validation purposes. Real gas formulations have been used based on the NIST REFPROP database. The validation is based on a design from the literature, and the results demonstrate close agreement the reference geometry and thermodynamic parameters. The total-to-total efficiencies of the reference turbine designs were 72% and 79%. Following the validation exercise, an optimization process was performed using a controlled random search algorithm with the turbine efficiency set as the figure of merit. The optimization focuses on the R245fa working fluid since it is more suitable for the operating conditions of the proposed cycle, enables an overpressure in the condenser and allows higher system efficiency levels. The R236fa working fluid was also used for comparison with the literature, and the reason is the positive slope of the saturation curve, somehow is possible to work with lower temperatures. Key preliminary design variables such as flow coefficient, loading coefficient, and length parameter have been considered. While several optimized preliminary designs are available in the literature with efficiency levels of up to 90%, the preliminary design choices made will only hold true for machines operating with ideal gases, i.e. typical exhaust gases from an air-breathing combustion engine. For machines operating with real gases, such as organic working fluids, the design choices need to be rethought and a preliminary design optimization process needs to be introduced. The efficiency achieved in the final radial turbine design operating with R245fa following the optimization process was 82.4%. A three-dimensional analysis of the flow through the blade section using computational fluid dynamics was carried out on the final optimized design to confirm the preliminary design and further analyze its characteristics.

Recently, the CO2 power cycle has attracted attention because of tightening environmental regulations. The turbine is a factor that greatly affects the efficiency of the cycle. The radial outflow turbine is a turbomachine with the various advantages of an axial flow turbine and a radial inflow turbine, but the design theory for the turbine is uncertain. In this study, a preliminary design algorithm for a radial outflow turbine with a multi-stage configuration is presented. To verify the preliminary design algorithm, a preliminary design for a two-stage radial outflow turbine for a CO2 power cycle was carried out, and a computational fluid dynamic analysis was performed. Consequently, values close to the target performance were obtained, but blade optimization was performed to obtain more satisfactory results. The final geometry of the radial outflow turbine was obtained through optimization considering the blade exit angle related to the deviation angle, blade maximum thickness-true chord ratio, and incidence angle. In the final geometry, the error rates of power (W˙), efficiency (ηts), and pressure ratio (PRts) between target performance and computational fluid dynamic results were improved to 5.0%, 4.8%, and 1.8%, respectively. The performance and flow characteristics of the initial and final geometries were analyzed.

This paper proposes an integrated design and optimization approach for radial inflow turbines consisting of an automated preliminary design module and a flexible three-dimensional multidisciplinary optimization module. The latter was constructed by an evolution algorithm, a genetic algorithm-assisted self-learning artificial neural network and a dynamic sampling database. The 3-D multidisciplinary optimization approach was validated by the original T-100 turbine and the T-100re turbine obtained from the automated preliminary design approach, for maximizing the total-to-static efficiency and minimizing the rotor weight while keeping the mass flow rate constant and stress limitation satisfied. The validation results indicate that the total-to-static efficiency is 89.6%, increased by 1.3%, and the rotor weight is reduced by 0.14 kg (14.6%) based on the T-100re turbine, while the efficiency is 88.2%, increased by 2.2% and the weight is reduced by 0.49 kg (37.4%) based on the original T-100 turbine. Moreover, the T-100re turbine shows better performance at the preliminary design stage and conserves this advantage to the end, though both the aerodynamic performance of the T-100 and the T-100re turbine are improved after 3-D optimization. At the same time, it is implied that the preliminary design plays an essential role in the radial inflow turbine design process, and it is hard for only 3-D optimization to get a further performance improvement.