Meanline Model Research Articles

Equation-Oriented Meanline Method for Axial Turbine Performance Prediction Under Choking Conditions

Abstract Meanline models play a crucial role in turbine design and system-level analyses, facilitating rapid evaluation of design concepts and prediction of off-design performance. Most of the existing meanline methods are inadequate in predicting turbine performance under choking conditions. These models either neglect the impact of losses on choking, or increases the computational complexity significantly. This limitation is addressed in this work, presenting a novel meanline model. The choking state at each cascade is determined by maximizing the mass flow rate, while taking into account the effect of losses. Leveraging the method of Lagrange multipliers, the optimization problems are transformed into a set of equations that seamlessly integrate with the rest of the meanline model. The resulting system of equations is then solved simultaneously using efficient root-finding algorithms, resulting in fast and reliable convergence. Validation against experimental data from three different turbines demonstrates the model's ability to accurately predict mass flow rate, torque, and exit flow angles across single- and multi-stage turbines, with errors typically within ±2.5 % and ±5.0 % for mass flow rate and torque respectively, and within ±5 degrees for flow angles. The proposed approach represents a significant advancement in meanline modeling, offering improved accuracy and computational efficiency.

Supercritical Carbon Dioxide Mixing Loss Characteristics Near the Critical Point

Abstract This paper aims to study the mixing loss characteristic of sCO2 near the critical point and shed light on the non-ideal fluid effect on the mixing losses. As a simplified model of the mixing process in the trailing edge or tip leakage flow in turbomachines, a case of mixing in a constant area adiabatic duct involving two streams of parallel flows is studied by control volume analysis. Both perfect gas and non-ideal fluid calculations are carried out for comparisons. The isolated and coupled effects of the two mixing streams' temperature, velocity, and pressure differences on the loss are investigated. The study shows that non-ideal fluid mixing produces significantly higher losses when compared to the equivalent perfect gas estimation. It also reveals that the non-ideal fluid mixing loss is sensitive to the average thermodynamic states of the mixing streams. A significant variation of the mixing loss coefficient is reported if the static state of any of the two streams is near the critical point, which is mainly caused by the significant variation of the temperature gradient regarding the entropy along the isobar. The results also show that the change in the mixing loss due to the variation of one property difference between mixing streams is almost independent of the other property difference. The results from this simple case contribute to understanding the mixing loss behaviour differences between perfect gas and non-ideal fluids in sCO2 turbomachinery and hold significance for the development of mean-line models.

An efficient multi-fidelity simulation approach for performance prediction of adaptive cycle engines

Adaptive cycle engine (ACE) with multi-stream, modulated bypass ratio, and high-thrust/high-efficiency mode provides the capability of multiple mission adaptation for the next-generation aviation propulsion system. The low-fidelity zero-dimensional (0D) performance simulation method is commonly adopted in conventional engines such as turbofan and turbojet. However, it is hard to accommodate well to ACE with complex variable geometry schemes and strong interaction between components. This paper presents an efficient multi-fidelity simulation approach, often referred to as component zooming, for predicting the performance of ACE with the three-stream configuration. The one-dimensional (1D) mean-line models of the adaptive fan and low-pressure turbine (LPT) are integrated into the 0D ACE model by the iteratively-coupled method. The performance predicted by the multi-fidelity ACE models with different component zooming strategies is compared. The maximum deviations of thrust, specific fuel consumption, turbine inlet temperature, and bypass ratio between the 0D/1D Adaptive Fan/1D LPT coupled model and 0D ACE model are −10.8%, −4.4%, −5.4% (−75 K), and 1.6%, respectively, which are considerable and non-negligible for the application in the design stage of ACE. The computing time of all the multi-fidelity models is less than 2 minutes. The effects of the key aerodynamic parameters of the adaptive fan and LPT on the engine performance are also evaluated. The proposed approach provides a generic and efficient solution for multi-fidelity ACE performance prediction with acceptable computing resource requirements and time cost, which is applicable in the engine conceptual and preliminary design stage.

Turbocharger turbine map scaling for virtual engine use

Emissions requirements, performance expectations, and expanding range of fuels for off-road engines are broadening engine air system requirements. As part of reducing engine development cost and risk, virtual engine simulation is used to select architecture and components capable of covering a broad range of requirements through low risk changes to the turbocharger turbine. A method is presented for predicting turbine performance changes due to turbine housing area change, the most effective of these low risk changes, from available turbine map data. The method, developed from a mean line model, learns four simplified geometry parameters, three loss coefficients, and two maximum efficiency rotor inlet incidence coefficients from a training turbine map data set, then predicts a scaled turbine map for changes to a simplified geometry parameter associated with housing area. Reduced mass flow RMS errors less than 4.3% and efficiency RMS errors less than 5.2% are expected when generating scaled turbine maps with this method, which is additional 2% error for flow and 3% error for efficiency over that expected when modeling actual turbine map data.

Mean-line analysis and optimal design of turbines using a proper algorithm for choked conditions

Compressible flow turbines usually work under choked conditions, requiring an analysis for the performance estimation. The Mean-line modeling is a fast and accurate method extensively used for the analysis and design purposes. However, it has not already been well-investigated for axial flow turbines specially in choked conditions. The present study investigates the issue from three novel aspects. First, a detailed study is accomplished on the inconsistencies of Mean-line method respect to the physics of real flows. It is discussed that the conditions related to maximum mass flow rate through a nozzle and the Mach number one at the throat are different. In fact, the latter condition is not quite physical. Second, a complete algorithm is utilized to implement the aforementioned considerations for the analysis of turbines. This algorithm includes an innovative Blade Solution Algorithm (BSA) and Turbine Solution Algorithm (TSA). The BSA solves the blade rows of turbine using the basic laws of Physics and real-gas properties. In the TSA, a robust and efficient procedure is presented so the solution of turbine converges in wide ranges of boundary conditions with minimum iterations. The results demonstrate that the algorithm generate close maps to the previous studies. Eventually in the third part, since a fast and robust Mean-line algorithm is crucial in optimization, the code is utilized for a design based on optimization using the Genetic Algorithm. In this procedure, all geometrical parameters are optimized as decision parameters rather than the use of old and approximate correlations. This is done along with novel constraints, which not only maximizes efficiency, but also puts the output power, mass flow rate and turbine size in appropriate ranges. The optimization results in a 3.5% rise in efficiency.

Optimization design of radial inflow turbine combined with mean-line model and CFD analysis for geothermal power generation

It is a considerable challenge to determine the key parameters affecting the efficiency and propose an accurate loss prediction model for radial flow turbine design. In current investigation, a one-dimensional mean-line model combined with particle swarm optimization algorithm and Kriging response surface surrogate model based on 3D numerical results were proposed to optimize radial flow turbines and evaluate performance. The loss model was carried out to analyze the relationship between geometric parameters, operating conditions and turbine performance. CFD numerical simulations were employed to revealed the mechanism of enhancing the turbine performance. The total-static efficiency was increased from 88.5 % to 91.7 %, and the clearance loss and passage loss were reduced by 18.4 % and 35.8 %, respectively,by optimized design. It is attributed to mitigate the curvature-induced boundary layer separation and vortex at the outlet, which reduces the secondary flow losses.The correlation between the predicted values of the Kriging response surface and the numerical results was up to 98.3 %. The results showed that the angle of attack was in the range of -10-0°, the blade has less influence on the flow loss. The current study effectively combined the flow path structure parameters and flow characteristics to realize the efficient optimization of ORC turbine.

Aerodynamic analysis of a 1.5 kW two-stage counter-rotating partial-admission impulse turbine for small-scale power system with a high expansion pressure ratio

Partial-admission impulse turbine is suitable for small-scale power cycles with a high expansion pressure ratio (EPR) and a low mass flow rate. However, the exit velocity of a single-stage turbine is very high, leading to a large exit loss. A new two-stage counter-rotating impulse turbine has been developed to recover the exit loss, which has a novel structure without stator between the two rotors. However, the internal flow characteristic of such a turbine is still unclear. In this study, the aerodynamic performance of the two-stage counter-rotating partial-admission impulse turbine is analyzed. The internal aerodynamic characteristics are estimated via CFD simulation. First, the geometric parameters are determined based on the mean-line model. Then, the characteristic line method is adopted to design the blade profile of the first supersonic stage based on the vortex flow theory. Subsequently, the performances are estimated under the design and off-design conditions via 3D CFD simulation. The results indicate that the modified convergent-divergent supersonic nozzle exhibits a better adaption with the impellers. The load is principally imposed on the upper zone of the blades. The power output of the turbine reaches 1501.3 W with an EPR of 52 and an efficiency of 45.99 % at the design point and the power of the first impeller accounts for 76.5 %. The mass flow rate increases almost linearly with the augmentation of the turbine inlet pressure. The power output proportion of the second impeller may arrive at 27.63 % under off-design conditions, showing the addition of the second stage can improve the turbine performance evidently.

A New Integrated Model for Simulating Adaptive Cycle Engine Performance Considering Variations in Tip Clearance

The low-fidelity simulation method cannot meet the requirements for predicting the performance of an adaptive cycle engine (ACE), especially when considering tip clearance variations in the compression and expansion systems. The tip clearances of the components of an ACE, such as the adaptive fan and turbine, vary drastically under different operating conditions. Though the tip clearance significantly impacts the engine’s performance, including its thrust and fuel consumption, variations in tip clearance are not considered in traditional ACE simulation models. This paper developed a new integrated model for predicting ACE performance, including multi-fidelity simulation models of the components and a newly developed, simplified model for predicting tip clearance. Specifically, the integrated model consists of a zero-dimensional (0D) engine performance simulation model, a three-dimensional (3D) adaptive fan numerical simulation model, a one-dimensional (1D) low-pressure-turbine (LPT) mean line model, and a multi-dimensional (MD) tip clearance prediction model. The integrated model solved the problem of considering the impact of tip clearance on an ACE and further improved the accuracy of thrust and fuel consumption predictions. Specifically, considering variations in the tip clearances under the design conditions, the differences in the thrust and specific fuel consumption (SFC) of the ACE are 1% and 0.3%, respectively. In conclusion, the integrated model provides a useful tool for evaluating the performance of an ACE while considering tip clearance variations.

Performance estimation of multi-stage cooled axial flow turbines under choked conditions

Development of a fast and accurate tool to estimate the performance of axial flow turbines in all range of working conditions including choked region is of great interest in the design steps of turbines. Mean-line (one-dimensional) analysis is one of the solutions that is computationally cost-effective along with producing accurate results. However, the development of a mean-line model that able to solve the flow in a choked turbine (one-row chocking and multi-row choking) is a challenging problem. This study presents a new algorithm for mean-line analysis of axial flow turbines with a set of well-posed boundary conditions, i.e., the inlet total pressure, the inlet total temperature, inlet flow angle, and outlet static pressure and calculates the flow condition through the turbine row-by-row. The proposed algorithm is implemented in an object-oriented C++ code named Axial Turbine Simulator (ATSim). The results of ATSim program is validated and verified under various working conditions, e.g., low and high-pressure ratios (choking condition), for four different turbine configurations including two uncooled single-stage turbines, an uncooled two-stage turbine, and a cooled three-stage turbine. ATSim provide good consistency with previous experimental and numerical studies. Moreover, the results show that ATSim is capable of estimating the performance of the turbine in a very short time over a wide range of working conditions, including choking (one-row choking or multi-row choking) region.

Design of the Organic Rankine Cycle for High-Efficiency Diesel Engines in Marine Applications

Over the past few years, fuel prices have increased dramatically, and emissions regulations have become stricter in maritime applications. In order to take these factors into consideration, improvements in fuel consumption have become a mandatory factor and a main task of research and development departments in this area. Internal combustion engines (ICEs) can exploit only about 15–40% of chemical energy to produce work effectively, while most of the fuel energy is wasted through exhaust gases and coolant. Although there is a significant amount of wasted energy in thermal processes, the quality of that energy is low owing to its low temperature and provides limited potential for power generation consequently. Waste heat recovery (WHR) systems take advantage of the available waste heat for producing power by utilizing heat energy lost to the surroundings at no additional fuel costs. Among all available waste heat sources in the engine, exhaust gas is the most potent candidate for WHR due to its high level of exergy. Regarding WHR technologies, the well-known Rankine cycles are considered the most promising candidate for improving ICE thermal efficiency. This study is carried out for a six-cylinder marine diesel engine model operating with a WHR organic Rankine cycle (ORC) model that utilizes engine exhaust energy as input. Using expander inlet conditions in the ORC model, preliminary turbine design characteristics are calculated. For this mean-line model, a MATLAB code has been developed. In off-design expander analysis, performance maps are created for different speed and pressure ratios. Results are produced by integrating the polynomial correlations between all of these parameters into the ORC model. ORC efficiency varies in design and off-design conditions which are due to changes in expander input conditions and, consequently, net power output. In this study, ORC efficiency varies from a minimum of 6% to a maximum of 12.7%. ORC efficiency performance is also affected by certain variables such as the coolant flow rate, heat exchanger’s performance etc. It is calculated that with the increase of coolant flow rate, ORC efficiency increases due to the higher turbine work output that is made possible, and the condensing pressure decreases. It is calculated that ORC can improve engine Brake Specific Fuel Consumption (BSFC) from a minimum of 2.9% to a maximum of 5.1%, corresponding to different engine operating points. Thus, decreasing overall fuel consumption shows a positive effect on engine performance. It can also increase engine power output by up to 5.42% if so required for applications where this may be deemed necessary and where an appropriate mechanical connection is made between the engine shaft and the expander shaft. The ORC analysis uses a bespoke expander design methodology and couples it to an ORC design architecture method to provide an important methodology for high-efficiency marine diesel engine systems that can extend well beyond the marine sector and into the broader ORC WHR field and are applicable to many industries (as detailed in the Introduction section of this paper).

A comparative study of mean-line models based on enthalpy loss and analysis of a cavity-structured radial turbine for solar hybrid microturbine applications

Lightweight components are essential for the future of the energy and aerospace fields. This paper presents an innovative radial turbine design that utilizes a cavity structure on the rotor for solar hybrid microturbines. The performance of the cavity-structured radial turbine is studied using mean-line models, computational fluid dynamics (CFD), and finite element analysis (FEA) simulations. The radial turbine is compared using air and supercritical carbon dioxide (sCO2) as the working fluid. The mean-line models based on enthalpy losses from recent literature are validated using commercial code Rital and CFD results. The impact of the isentropic velocity ratio (νs) and absolute flow angle at the rotor inlet (α1) on the optimum design for the rotor radial turbine is also demonstrated. A comparative loss enthalpy breakdown on the rotor is examined, such as incidence loss, passage loss, trailing edge loss, clearance loss, exit loss, and windage loss. The results show that the recent mean-line models based on enthalpy losses can accurately estimate the stage efficiency for both air and sCO2 turbines. By comparing the simulation results obtained from 3D-CFD and mean-line models, the efficiency prediction deviation is within an acceptable range of tolerance for both turbines when comparing the results obtained from 3D-CFD and mean-line models. The FE analysis reveals that the maximum stress decreased significantly for the air and sCO2 turbine after the rotor blade was added using the cavity structure inside. The maximum stress value on the rotor with the cavity structure design is still below the yield strength of the material limits. Furthermore, after the variations of the cavity structure design were added to the rotor blade of both turbines, the results were promising when the dangerous resonance at below 4EO (Engine Order) was minimized. The results of this study provide a promising direction for the development of high-efficiency and lightweight turbines in the energy and aerospace fields.

A Review on the Preliminary Design of Axial and Radial Turbines for Small-Scale Organic Rankine Cycle

Organic Rankine cycle (ORC) is an effective technology to harness low-grade energy. Turbine, as a key component of ORC, takes advantages of its high efficiency and compact size compared with other expanders. Currently, developing suitable turbines with a high performance and a low cost is one of the bottlenecks for wide applications of various ORCs. In this context, technical progress on radial inflow turbines (RITs), axial turbines (ATs), and radial outflow turbines (ROTs) is introduced, and loss models used in the preliminary design are compared, especially for small-scale ORCs. RIT is recommended for medium and small ORCs with an expansion pressure ratio of <10. The power outs and rotational speeds of the designed RITs spanned the ranges of 9.3–684 kW and 3000–114,000 r/min with an efficiency of 56.1–91.75%. In comparison, the power outputs and speeds of ATs were 3–2446 kW and 3000–91,800 r/min with an efficiency of 63–89.1%. AT is suitable for large-scale ORCs with a power output of greater than hundreds of kW. However, AT with impulse stages is feasible for small-scale ORCs when the pressure ratio is high, and the mass flow rate is small. The power outputs of the designed ROTs were relatively small, at 10–400 kW with a speed of 7200–42,700 r/min and an efficiency of 68.7–85%. For organic working fluids with a large expansion pressure ratio, ROT might be employed. Conventional mean-line models may neglect the effects of supersonic flow, which will be encountered in many ORC turbines. Therefore, adequate models for supersonic expansion loss and shock loss need to be added. Meanwhile, a proper multivariable optimization algorithm such as a gradient-based or stochastic search method should be selected. Finally, the challenges and potential research directions are discussed. The outcomes can provide some insights for the development of ORC turbines and the optimization of ORC systems.

Using Machine Learning for Loss Prediction in a Hybrid Meanline Modeling Method to Deliver Improved Radial Turbine Performance Prediction

Abstract Low fidelity modeling approaches remain attractive due to an unrivaled ability to predict full turbine performance maps quickly compared to high-fidelity approaches such as computational fluid dynamics (CFD), especially in the preliminary design process. As improvements in performance on a component level approach a point of diminishing returns, the ability to efficiently optimize the complete charging system for a given duty is a topic attracting significant research interest. In the case of turbocharging applications, existing engine and powertrain simulations require turbine maps to calculate the turbine performance, which are usually obtained from experimental testing. Unfortunately, the need for extrapolation is unavoidable because of the limited range of testing data available, leading to inaccuracies especially at off-design conditions. To enable intensive modeling and optimization of complete vehicle powertrains for different drive cycles, the current piece of work seeks to combine the advantages of machine learning techniques and physical meanline modeling to facilitate faster, more accurate predictions of complete turbocharger maps. This paper presents a novel methodology for turbocharger turbine rotor and nozzle performance prediction based on hybrid modeling. The turbine rotor and nozzle were parameterized to conduct CFD simulations for a wide variety of turbine geometries, which were used to form a database to train an artificial neural network (ANN). The predicted losses provided by the ANN were then utilized in the meanline code, substituting for the conventional empirical loss models. As well as removing the need for empirical loss models, modifications were undertaken to the meanline approach to further enhance modeling accuracy. First, in order to accurately characterize the stage mass flow capacity, the losses occurring in the nozzle and rotor were subdivided into those occurring before and after the throat. A second novel aspect is that the aerodynamic blockage level at the rotor throat was implemented as a variable rather than a constant value. By training the ANN to predict the variation of blockage with geometry and operating condition, a more accurate depiction of the changing secondary flow fields could be achieved. The capabilities of the hybrid meanline modeling method were evaluated on several unseen test cases. The resulting predictions of efficiency and mass flowrate demonstrated strong correlation with CFD results and experimental test results. The hybrid meanline modeling method therefore displays great potential in wide range radial turbine performance prediction with enhanced accuracy in comparison to traditional approaches.

A study on one-dimensional model correction for axial-flow compressors based on measurement data

In this study, a method for correcting a one-dimensional (1D) meanline model for axial-flow compressors using measured data and its effectiveness were described. The proposed method was evaluated for a 6-stage axial-flow compressor with variable guide vanes. In the compressor performance test, the rotating speed, the total pressure for each stage, and the total temperature at the inlet and outlet were measured. A compressor 1D meanline model was constructed using the empirical equations suggested in the existing research literature. Correction factors for the deviation angle and overall efficiency were applied to match the data measured in the performance test and the predicted values from the 1D model. Correction factors were calculated for each measurement point. The calculated correction factors were generated as a function according to the operating conditions using an artificial neural networks model. Moreover, a criterion for defining the compressor surge point in the 1D model was generated as a function of the diffusion factor and the relative Mach number of the inlet. By applying the generated functions to the existing compressor prediction model, the results at the operating point not used for model correction were compared. As a result, it was confirmed that a corrected 1D performance prediction model with high prediction accuracy can be obtained through the proposed method.

Optimization of an Organic Ranking Cycle Radial Turbine Using a Reduced-Order Model Coupled With Computational Fluid Dynamics

Abstract This paper presents the geometry optimization of a single stage radial turbine for an organic ranking cycle (ORC) system operating over a pressure ratio of 9. The specific fluid used in this investigation is R1233zd (E), but the methodology applies to other organic fluids as well. The ORC system is used to recover excess waste heat from the operation of an offshore oil and gas platform in the gulf of Thailand and its conditions will be replicated at pilot plant level. The geometry is optimized for the highest total-to-static efficiency using nongradient based algorithms to allow for wide design space. Firstly, a one-dimensional meanline geometry is optimized, which is followed by a computational fluid dynamics (cfd) optimization in three-dimensional using a parameterized model. cfd is used to validate and calibrate the meanline model as well as to understand the flow and the sensitivity of the design parameters not captured by the low-order model. Moreover, the flow field of the successful designs is analyzed by cfd to identify the main flow structures that explain the difference in performance among the designs. The nonideal gas thermophysical properties of R1233zd (E) are calculated using equations of state to account for the nonideal gas behavior.

Design and off-design system simulation of concentrated solar super-critical CO2 cycle integrating a radial turbine meanline model

The proper design of a Concentrated solar power (CSP) plant and the associated thermal energy storage requires a careful analysis of the yearly expected irradiance and environmental conditions. System simulations based on accurate components models allow the prediction of the performance of the plant and the analysis of the components interactions. The simulations of various scenarios provide information that will help tuning the design of the components to improve the performance of the whole system at design and off-design conditions. In this paper, the focus is set on the radial turbine expander which is one of the most important component. Classical system simulation approaches use map based performance model for the turbine. This require to generate the performance map either with meanline models, CFD simulations or experiments. This is not very convenient when iterating on the system design and if the actual turbine does not exist yet. In this work, a meanline model for radial inflow turbine operating with real gas has been implemented in MODELICA language for the first time to the authors’ best knowledge. This turbine model has been coupled with the available CSP sCO2 Brayton cycle model in MODELON ThermalPower library. A parametric study on a virtual test bench show the turbine performances for various rotational speed and inlet guide vane angle. The study focus then on the performance prediction of on and off design of the system with a 8 MW turbine obtained with a simple preliminary design calculation. The investigations showed that for the varying load conditions in the solar plant system, an improved operating point has been identified by adjusting the rotational speed and the inlet guide vane angle. Future work will focus on the use such system model with multi objective meta heuristic optimization.

Design and performance analysis of a cryofan for helium closed loop cooling systems

Cryofan is the most vital component for helium closed loop cooling systems, which can provide the circulatory force of the gaseous helium. Thus, it is essential to develop a high efficiency cryofan in order to improve the energy efficiency of the cooling system. In this paper, a cryofan is designed for a helium closed loop cooling system of superconducting magnets. The design inlet temperature and total pressure ratio are 80 K and 1.1 respectively. The design mass flow rate is 17.5 g·s−1. A novel empirical model for incidence loss is proposed to calculate the incidence flow loss. A mean-line design and analysis model based on flow loss models is established to design and predict the performance of the cryofan. Based on the mean-line design results, a 3D design approach is proposed to design the detailed 3D geometry of the cryofan. Furthermore, 3D CFD simulations are conducted in order to predict the performance in design condition and off-design conditions, and further verify the accuracy of the mean-line model. The results indicate that the proposed novel empirical model for incidence loss is accurate and reliable, and an efficient cryofan can be designed and analyzed conveniently through applying the proposed mean-line model and 3D design method.

Study on a flow-field-based meanline model of nozzled twin-entry mix-flow turbine

Variable geometry twin-entry turbine has advantages in fuel economy, low-end torque, emission and turbo-engine matching of internal combustion engine. The reliability of performance prediction method for nozzled twin-entry turbine is heavily dependent on the understanding of flow mechanism of the turbine which is always confronted by time-dependent unequal admissions. This paper establishes a new meanline model of a nozzled twin-entry turbine based on the internal flow features. Firstly, flow mechanism of the twin-entry turbine with a vaned nozzle under different admissions is investigated via an experimentally validated CFD method. Results clearly demonstrate that the flow distortion in spanwise direction caused by unequal admissions notably influences the turbine efficiency discrepancy between symmetric unequal admissions, especially the two partial admissions. The evolution of flow distortion in the nozzle passage is the key to the performance discrepancy, which is impossible to be considered by a conventional performance model of a nozzled twin-entry turbine. Inspired by this, a newly-designed meanline model, named ‘parallel nozzle’ is proposed. Specifically, a nozzle passage is divided into two parallel sub-passages in spanwise direction to consider the flow distortion in nozzle passage. The model is validated against the detailed CFD results in terms of both overall performance and detailed flow parameters over different admissions. Results prove that turbine performance and flow parameters are well predicted by the model. Specifically, the influence of admissions on nozzled twin-entry turbine performance and flow parameters can be predicted by the method in satisfying accuracy.

Mean-line model development for off-design performance prediction of transonic axial compressor of an industrial gas turbine based on computational fluid dynamics database

In this work, a mean-line model with the row-by-row stacking scheme is developed to simulate the off-design operation of a multi-stage transonic axial compressor of an industrial gas turbine. A database of computational fluid dynamics (CFD) simulation results validated with the field data is generated at different rotating speeds and pressure ratios by using CFD simulation tools and available detail geometry of the studied compressor. The compressor characteristic parameters including inlet/exit blockage factor, deviation angle parameter, rotor temperature and pressure coefficients, and the pressure loss of the stator for all stages, plus variable inlet guide vane, are extracted from CFD simulation results. Based on analytical/empirical relations in the literature, a generic formulation for the characteristic parameters is defined as a function of airflow parameters such as inlet Mach number, inlet flow angle, and velocity ratio. Since the accuracy of this type of model depends on the formulated characteristic parameters, and due to the error propagation potential of the sequential stacking solutions, a multi-objective optimization program is developed to specify the coefficients and exponent values of the generic formulations. The functionality of characteristic curves versus airflow parameters for different compressor rows is comprehensively investigated. The comparison between the results of the mean-line model and CFD simulations shows the high accuracy of the model. The developed model can be used in applications such as condition monitoring of in-service gas turbines, studying the effects of rescheduling the variable stator vanes, and investigating the wet compression process.

Equivalent model for an axial compressor used for aero engines based on 1D and 3D analytical models and performance data

This paper proposes a method to generate an equivalent model for predicting compressor performance by correcting a one-dimensional (1D) meanline analysis model based on the results of three-dimensional computational fluid dynamics (3D CFD) and compressor performance at an engine operating point. By comparing the results predicted by the 1D and 3D analysis methods, the compressor operating region and empirical model that needs improvement in the 1D meanline model are identified. As a result, the off-design profile loss model and the model for the incidence angle in the choking condition are selected as models that need improvement; the models are adjusted based on the 3D CFD analysis results. Correction factors for deviation angle, minimum loss incidence angle, and total loss coefficient are proposed. The correction factors are calculated using an iterative method to match the result for the 1D meanline model and the compressor performance at an engine operating point. The method proposed is applied to a three-stage axial compressor used for an aero engine. This confirms that not only compressor performance near the operating point, but also performance near surge and choking, are well predicted.