Multistage Configurations Research Articles

A comprehensive review of effective parameters to improve the performance of the Savonius turbine using a computational model and comparison with practical results

Amidst growing global concerns over climate change and escalating greenhouse gas emissions from fossil fuels, the pursuit of renewable energy sources has become critical. This study focuses on harnessing hydropower using Savonius turbines, which are known for their efficiency in generating energy at lower flow rates. However, the intrinsic low efficiency of these turbines necessitates precise optimization tailored to specific river or channel conditions. In this research, we optimized the performance of Savonius turbines by analyzing key parameters such as the height-to-diameter ratio, blade twist, and the integration of multi-stage configurations with deflectors. Our findings reveal significant efficiency improvements through strategic modifications. Specifically, by reducing the height-to-diameter ratio from 1.2 to 0.8 and maintaining a Tip Speed Ratio (TSR) of 0.6, the power coefficient increased by 15%, from 0.33 to 0.38. Further optimization was achieved by adjusting the blade twist angle, with an increase in power coefficient up to an optimal angle of 45°, beyond which efficiency declined. Implementing a two-stage turbine setup with a 90-degree phase difference between stages further improved the power coefficient to 0.51 at the same TSR. Additionally, the use of deflectors, particularly at a 90° angle, significantly boosted the power coefficient, highlighting their effectiveness in optimizing water flow impact on the turbine. This comprehensive study not only advances the understanding of Savonius turbine optimization but also contributes to broader renewable energy applications. The research offers critical insights into sustainable hydroelectric power generation, providing practical solutions to enhance turbine performance for real-world applications.

Biogas upgrading to biomethane with zeolite membranes: Separation performance and economic analysis

Biogas represents an important renewable source alternative to fossil fuels, which can significantly contribute to the reduction of global warming and the gradual decarbonisation. In this work, the purification of CH4 and CO2 from a biogas mixture was investigated using DD3R zeolite membrane modules, as a possible solution to replace the traditional techniques at higher environmental impact (i.e., solvent absorption and cryogenic distillation). Multistage membrane configurations operating at 25°C and 30 bar were proposed and explored to get highly pure biomethane (concentration of 98 %) and carbon dioxide (concentration of 99.5 %), imposing a recovery of both the species higher than 90 %. Then, an economic analysis was carried out, evaluating the economic potential of each configuration as a function of several parameters, such as membrane module cost, biomethane selling price, CO2 permeance, CO2/CH4 selectivity, feed flow rate and pressure. The multistage schemes were found to be promising in a wide range of zeolite membrane module cost (i.e., up to 2000 $/m2), providing positive values of the economic potential, due to the good recovery of both the components, which produced high revenues. The increment of the CO2 permeance and, especially, of the feed flow rate (i.e., plant size) allowed for a more profitable process. In particular, if feed flow rate increased from 100 to 1000 Nm3/h, the economic potential would grow of about 12 times, from 113 to 1370 thousand dollars per year. Hence, this preliminary economic assessment showed that zeolite membranes can be successfully used in biogas treatment to get pure CH4 and CO2. Such an analysis can be applied to any membrane materials, once permeance and selectivity are fixed.

Analyzing Unsteady Turbomachinery Flow Simulations With Mixing Entropy

Abstract The prediction of unsteady aerodynamic loads is a central problem during the design of turbomachinery. Over the last 20 years, harmonic balance methods have been shown to be highly efficient for this task. A CPU-cost optimal setup of a harmonic balance simulation, however, requires knowledge of relevant harmonics. In the case of a single blade row with a periodic disturbance this question amounts to the classical problem of harmonic convergence, a problem which is solely due to the nonlinearity of the unsteady flow physics. In contrast, for multi-stage configurations, the choice of harmonics is further complicated by the fact that the interactions of disturbances with blade rows may give rise to a vast spectrum of harmonics that possibly have important modal content, e.g., Tyler–Sofrin modes. The aim of this paper is to show that the mixing entropy attributed to circumferential modes of a given harmonic can serve as a disturbance metric on the basis of which a criterion could be derived whether a certain harmonic should be included or not. The idea is based on the observation that the entropy due to the temporal and circumferential mixing of the flow at a blade row interface may be decomposed, up to third-order terms, into independent contributions from different frequencies and mode orders. For a given harmonic balance (and steady) flow result, the mixing entropy attributed to modes that are simply mixed out, rather than resolved in the neighboring row, is shown to be a natural indicator of a potential inaccuracy. We present important features of the mixing entropy for unsteady disturbances, in particular a close relationship to sound power for acoustic modes. The problem of mode selection in a 1.5-stage compressor configuration serves as a practical example to illustrate our findings.

Numerical investigation on non-linear streaming effects in a two-stage coaxial pulse tube cryocooler

Stirling pulse tube cryocoolers (PTC) are widely used in aerospace applications for the cooling of infrared sensors and for filtering background thermal noise in the astro-imaging devices, etc. Present investigation aims to use numerical methods to demonstrate the nonlinear fluid flow, heat transfer, and vortex generation phenomena in a two-stage coaxial type inertance pulse tube cryocooler. The numerical simulation is conducted using commercially available Fluent® code for both single-stage and multi-stage configurations to show nonlinear processes with varying heat load conditions. It has been noticed that the width of the vortex produced inside the pulse tube grows with an increase in heat load capacity. This undesirable flow conditions yields an adverse effect in the cooling behavior and reduces overall performance of cryocooler with higher heat load. Additionally, streamlines, stream function, pressure and temperature variation plots are given for both stages with different heat load capacity to substantiate our results.

Continuous polyhydroxybutyrate production from biogas in an innovative two-stage bioreactor configuration.

Biogas biorefineries have opened up new horizons beyond heat and electricity production in the anaerobic digestion sector. Added-value products such as polyhydroxyalkanoates (PHAs), which are environmentally benign and potential candidates to replace conventional plastics, can be generated from biogas. This work investigated the potential of an innovative two-stage growth-accumulation system for the continuous production of biogas-based polyhydroxybutyrate (PHB) using Methylocystis hirsuta CSC1 as cell factory. The system comprised two turbulent bioreactors in series to enhance methane and oxygen mass transfer: a continuous stirred tank reactor (CSTR) and a bubble column bioreactor (BCB) with internal gas recirculation. The CSTR was devoted to methanotrophic growth under nitrogen balanced growth conditions and the BCB targeted PHB production under nitrogen limiting conditions. Two different operational approaches under different nitrogen loading rates and dilution rates were investigated. A balanced nitrogen loading rate along with a dilution rate (D) of 0.3 day-1 resulted in the most stable operating conditions and a PHB productivity of ~53 g PHB m-3 day-1 . However, higher PHB productivities (~127 g PHB m-3 day-1 ) were achieved using nitrogen excess at a D = 0.2 day-1 . Overall, the high PHB contents (up to 48% w/w) obtained in the CSTR under theoretically nutrient balanced conditions and the poor process stability challenged the hypothetical advantages conferred by multistage vs single-stage process configurations for long-term PHB production.

Analysis of typical chloride solution treatment by osmotically assisted reverse osmosis for evaluating application potential in geothermal reinjection well protection

Ions in geothermal water is one of the main inducements causing well corrosion and fouling problems, which sequentially increases maintenance cost and shortens facility lifespan. This work proposed to use split co-current osmotically assisted reverse osmosis to pre-treat geothermal water into diluted and concentrated solutions after heat utilization, for achieving internal dilution and ion enrichment purposes simultaneously. By establishing the mathematical model and calculation procedure under full water permeation, the discharge properties and energy consumption performance of single and multi-stage configurations to treat 4 typical chloride solutions (NaCl, KCl, CaCl2 and MgCl2) in geothermal water are mathematically analyzed. Beneficial from the inlet split of solute amount and water permeation ability under any appliable hydraulic pressure difference, the system is capable to treat salt water into diluted and concentrated solutions effectively. It is estimated that concentrated side achieves more significant concentration variance than diluted side, for it experiences steeper variance rate with the decreasing of solution volume. Upgrading single stage to multi-stage configuration, the treatment degree can be further enhanced especially as the concentration of inlet solution is high, but this will induce the continuous accumulation of energy consumption generated by the water permeation at each stage as expense.

The Potential of Multi-stage Pressure Retarded Osmosis for Blue Energy Harvesting

Objective: This study aims to investigate the potential benefits of using different multi-stage and multi-pass flow configurations for improving the efficiency of the pressure-retarded osmosis (PRO) process, which generates energy by utilizing the difference in osmotic pressure between two salinity solutions. Methods: To achieve the objective, the study used a numerical simulation based on the solution diffusion model. A flat sheet forward osmosis membrane was simulated to investigate the potential of the proposed multi-stage PRO configurations. Results: The results of the simulation showed that the multi-stage PRO arrangement generated 18% more power than the single-stage PRO system. Additionally, the multi-pass arrangement resulted in a 58% increase in power output. Conclusion: This study provides important insights into the development of optimized PRO membrane and module configurations to improve the efficiency of energy generation. The findings highlight the potential benefits of multi-stage and multi-pass flow configurations, which can help to advance the field of renewable energy generation using the PRO process.

Novel multi-stage vortex cooling with bypass for turbine blade leading edge design considering rotational effect

This work aims to comprehensively improve vortex cooling performance by suggesting a novel design in the blade leading edges of gas turbines. Under considering the effect of blade rotation, different multi-stage configurations with bypass are proposed. A series of validated calculations are performed based on solving steady-state Reynolds Averaged Navier-Stokes equations and the SST k-ω turbulence model. Heat transfer and flow characteristics of the different vortex cooling structures are analyzed at different rotational speeds. From the results, it can be concluded that: (1) under stationary conditions, compared to the single-stage model, the multi-stage design of vortex cooling can greatly enhance the heat transfer rate, and its average Nusselt number can be 87.6% higher, but the cost is the high total pressure loss. Nevertheless, the comprehensive thermal performance in the multi-stage configuration is still 7.2% higher at least. (2) When blade rotates, the heat transfer rates in all configurations generally decrease by the effect of the Coriolis force (at least 8.8% when rotational number is 0.072). With the increase of rotational speed, the unfavorable high friction loss in multi-stage design is also decreased. For example, the total pressure loss coefficient in multi-stage vortex cooling without bypass is decreased by 68.4% when Rotational number increases to 0.072. (3) The bypass design in the multi-stage model provides an effective way to control the heat transfer enhancement and total pressure loss. At a high rotational number of 0.072, using a bypass with a thickness of 0.25 mm, although the averaged Nusselt number drops by 9.9%, the decrease of total pressure loss reaches to 117%. This phenomenon implies that a proper multi-stage vortex cooling model with bypass design can significantly decrease the friction loss, at a negligible price of heat transfer reduction.

A generalized disjunctive programming model for multi-stage compression for natural gas liquefaction processes

The primary driver of operating costs in natural gas processes is the energy consumption of the compression system. Multistage compression configurations are commonly employed and hence play a vital role in optimization of natural gas processes. In this study, a generalized disjunctive programming model for multistage compression is formulated. The model is useful for both synthesis and optimization of multistage compression configurations. By using this approach, we further seek improvements in shaft work savings. The model relies on thermodynamic equations and is designed to minimize the consumption of shaft work. The model is handled by employing the logic-based branch and bound algorithm, eliminating the need for explicit conversion into a MINLP, which in turn leads to improved convergence and faster computational performance. The model solution yields optimal pressure levels, and hence stage shaft work consumptions. A case study of multistage compression for a prior optimized single mixed refrigerant (SMR) process obtained from literature is used to test the proposed model. The model’s outcomes are validated through simulation using the Aspen Hysys software. Savings in shaft work of atmost 0.0088%, 0.4433%, and 1.2321% are obtained for the two, three, and four stage compression systems respectively against the optimized base cases from literature.

Optimization-based technoeconomic comparison of multi-stage membrane distillation configurations for hypersaline produced water desalination

Unconventional oil and gas production raises concerns regarding sustainable management of high salinity wastewaters generated in this process. Membrane distillation (MD) is a thermal desalination process capable of treating hypersaline brines such as produced water. The low single pass recovery in MD systems operated in a single stage requires a large recycle stream to achieve the desired recovery, resulting in high energy consumption and operating cost. Multistage configurations in continuous recirculation operation mode offer the potential to reduce the energy intensity of MD systems. However, rigorous analysis is needed to assess the performance of MD configurations when operating in multi-stage mode. We present an optimization-based comparison of economic and energetic performance for five configurations of MD (including DCMD, AGMD, PGMD, CGMD, and VMD) operating in multi-stage continuous recirculation mode. Our findings demonstrate that multistage operation reduces the treatment cost and energy intensity of all MD configurations compared to single stage MD, with the greatest benefit for VMD and PGMD. AGMD with five stages outperforms other configurations with 3.58 $/m3feed treatment cost, followed by VMD, CGMD, DCMD, and PGMD with 3.8, 4.2, 5.4, and 9.06 $/m3feed treatment costs corresponding to twelve, eight, eight, and sixteen stages, respectively.

Design of multistage fixed bed reactors for SMR hydrogen production based on the intrinsic kinetics of Ru-based catalysts

In recent years, interest in the development of a hydrogen economy has increased, and the steam methane reforming (SMR) reaction, which yields so-called “gray” hydrogen, is expected to play a key role in hydrogen refueling stations (HRSs) in the interim before “green” hydrogen process is developed. For this purpose, compact and economical designs for small- to medium-scale SMR processes for HRSs are required. Herein, we investigated the intrinsic kinetics of a Ru-based catalyst using catalyst experiments and parametric estimation. In addition, reactor modelling was performed using a kinetic model with a special focus on multistage reactor configurations. The proposed reactor design showed an increase in the reactor energy supplied rate from 6.98 to 7.55 kW compared to the base case (single-stage reactor), and the conversion increased from 86.2% to 91.2%. Further, the drastic temperature drop owing to the strongly endothermic nature of the SMR reaction was reduced, and, thus, reactor stability was improved. The proposed novel design of a multistage reactor using a Ru-based catalyst will advance the development of the hydrogen economy.

Load Frequency Control (LFC) Strategies in Renewable Energy-Based Hybrid Power Systems: A Review

The hybrid power system is a combination of renewable energy power plants and conventional energy power plants. This integration causes power quality issues including poor settling times and higher transient contents. The main issue of such interconnection is the frequency variations caused in the hybrid power system. Load Frequency Controller (LFC) design ensures the reliable and efficient operation of the power system. The main function of LFC is to maintain the system frequency within safe limits, hence keeping power at a specific range. An LFC should be supported with modern and intelligent control structures for providing the adequate power to the system. This paper presents a comprehensive review of several LFC structures in a diverse configuration of a power system. First of all, an overview of a renewable energy-based power system is provided with a need for the development of LFC. The basic operation was studied in single-area, multi-area and multi-stage power system configurations. Types of controllers developed on different techniques studied with an overview of different control techniques were utilized. The comparative analysis of various controllers and strategies was performed graphically. The future scope of work provided lists the potential areas for conducting further research. Finally, the paper concludes by emphasizing the need for better LFC design in complex power system environments.

Loss Assessment of the NASA Source Diagnostic Test Configuration Using URANS With Phase-Lagged Assumption

Abstract This article presents the study of the Source Diagnostic Test fan rig of the NASA Glenn (NASA SDT). Numerical simulations are performed for the three different outlet guide vane (OGV) geometries (baseline, low count, and low noise) and three rotational speeds corresponding to approach, cutback, and sideline operating conditions, respectively. Unsteady Reynolds-averaged Navier–Stokes (URANS) approach is used. The in- and out-duct flow including the nacelle are considered in the numerical simulations, and results are compared against available measurements. Due to the blade count of the fan and OGVs (22 fan blades and either 54 or 26 blades for the OGVs), the simulation can only be reduced to half the full annulus simulation domain using periodic boundary conditions that still represents a significant cost. To alleviate this issue, a URANS with phase-lagged assumption is used. This method allows to perform unsteady simulations on multistage turbomachinery configurations including multiple frequency flows with a reduced computational domain composed of one single-blade passage for each row. The large data storage required by the phase-lagged approach is handled by a compression method based on a proper orthogonal decomposition (POD) replacing the traditional Fourier series decomposition (FSD). This compression method improves the signal spectral content especially at high frequency. Based on the numerical simulations, the flow field is described and used to assess the losses generated in the turbofan architecture based on an entropy approach. The results show different flow topologies for the fan depending on the rotational speed with a leading edge shock at high rotational speed. The fan boundary layer contributes strongly to losses with the majority of the losses being generated close to the leading edge.

Real-Time ML-Assisted Hardware-in-the-Loop Electro-Thermal Emulation of LVDC Microgrid on the International Space Station

For being the world’s largest low voltage direct current (LVDC) microgrid (MG) in space, the power generation and distribution systems aboard the International Space Station (ISS) employ a hierarchical assortment of electric power sources, energy storage, control devices, power electronics, and loads operating cooperatively at multifarious system dispositions and multi-stage configurations. At the early phase of design, for such time-critical systems, the trade-off between reliability and convergence rate of device modeling, varying accuracy requirements of control flows, and especially the implementation for real-time performance have brought new challenges and problems for testing and validation of the MG. One of the solutions presented by this paper is to use the hardware-in-the-loop (HIL) emulation, where the MG is emulated using the field-programmable gate array (FPGA) hardware platform. In parallel with the emulation effort, comprehensive modeling solutions for both large-scale photovoltaic (PV) solar array wings (SAWs) and nonlinear behavior model (NBM) of insulated-gate bipolar transistors (IGBTs) have been utilized based on machine learning (ML) concepts of artificial neural network (ANN) and recurrent neural network (RNN). Both system-level (validated by Matlab/Simulink) and device-level (validated by SaberRD) transient simulations are carried out, and the results exhibit high accuracy and fidelity of the models and significant improvements in execution speed and hardware resource consumption.

Loss assessment of the NASA SDT configuration using LES with phase-lagged assumption

This paper presents the numerical study of the Source Diagnostic Test fan rig of the NASA Glenn (NASA SDT). Large-Eddy Simulations (LES) based on a finite volume approach are performed for the three different Outlet Guide Vane (OGV) geometries (baseline, low-count and low-noise) and three rotational speeds corresponding to approach, cutback and sideline operating conditions respectively. The full stage and nacelle geometries are considered in the numerical simulations, and results are compared to available measurements. The NASA SDT configuration is equipped respectively with 22 fan blades and either 26 of 54 vanes depending on the OGV geometry. The simulation domain could only be reduced to half of the full annulus and would still be a significant cost for the LES. In order to reduce computational cost, an LES with phase-lagged assumption approach is used. This method allows to perform unsteady simulations of multistage turbomachinery configurations including multiple frequency flows with a reduced computational domain composed of one single blade passage for each row. The large data storage required by the phase-lagged approach is handled by a compression method based on a Proper Orthogonal Decomposition replacing the traditional Fourier series decomposition. This compression method improves the signal spectral content especially at high frequency. Based on the numerical simulations, the flow field is described and used to assess the losses generated in the turbofan configuration based on an entropy approach. The results show different flow topologies for the fan depending on the rotational speed with a leading edge shock at high rotational speed. The fan boundary layer contributes strongly to losses with the majority of the losses being generated close to the leading edge for the dissipation due to mean strains and close to the recirculation zone occurring on the suction side for the turbulent kinetic energy production.

Solid-liquid equilibrium of 3,3-dilauryl thiodipropionate/lauryl alcohol in melt crystallization and model based process design

Melt crystallization is a promising and widely used method for obtaining pure compounds. Nonetheless, separation of 3,3-dilauryl thiodipropionate (DLTP) has not yet been realized by melt crystallization. Solid-liquid equilibrium is the fundamental for the separation process design. In this work, we evaluated the feasibility of the purification of DLTP from the DLTP/lauryl alcohol (LA) binary mixture by melt crystallization technique. For this purpose, the solid-liquid equilibrium data were measured using differential scanning calorimetry (DSC) technique. The experimental data were correlated by Wilson, Margules-3-suffix and Non-Random Two-Liquid (NRTL) activity coefficient models to obtain the binary parameters of the three models. Eutectic composition and temperature were calculated using NRTL model, which were xLA = 0.961 (molar fraction) and 295.79 K, respectively. On the basis of the solid–liquid equilibrium, the multistage countercurrent separation configurations were proposed for the separation of the binary system. The formulated Mixed Integer Nonlinear Programming (MINLP) problem was solved using the branch-and-bound algorithm. The conceptual designs for multistage countercurrent configuration were derived based on MINLP optimization by comparing results at various conditions. Results showed that at least 3 crystallization stages with keff ≤ 0.4 are required to obtain the 99% (mass fraction) DLTP product within the initial concentration range from10% to 30% (mass fraction).

Numerical investigation of a novel multistage swirl cooling conception in blade leading edge of gas turbine

Swirl cooling is one of the latest and promising internal cooling strategies, which has been widely reported in the designs of the turbine blade leading edges. Based on the traditional single-stage swirl cooling configuration, this paper introduces a novel conception of multistage swirl cooling configuration (two and three stage), aiming to improve the cooling performances of the leading edges without increasing the cooling air consumption. In the new multistage configurations, the vortex chamber is divided into several stages, so that the tangential velocity of cooling air is significantly increased. To reveal the heat transfer and flow characteristics of cooling air in the multistage swirl cooling configuration, a series of numerical simulations are conducted by conjugate heat transfer algorithm under the realistic conditions of gas turbine operations and the real leading edge model of a VKI turbine blade. The numerical results indicate that: under the same coolant mass flow rate, the averaged Nusselt number in the three-stage swirl cooling structure is at least over 75% higher than that in the single-stage structure, and the Nusselt number distribution is also more uniform. At ReD = 40,000, the surface temperature averaged over the entire leading edge wall of the three-stage swirl cooling structure can be nearly 100 K lower than that in the single-stage one. The significant heat transfer enhancement of multistage swirl cooling is at the cost of a higher total pressure loss. However, if the bends connecting the adjacent stages are modified into round-shaped, the pressure loss can be significantly decreased, therefore the thermal performances of the multistage swirl cooling models are higher than that of the single-stage model.

The Combined Impacts of Leg Geometry Configuration and Multi-Staging on the Exergetic Performance of Thermoelectric Modules in a Solar Thermoelectric Generator

Abstract The performance of thermoelectric generators (TEGs) can be improved either by the adoption of multi-stage or tapered leg configuration. So far, a hybrid device that simultaneously uses both multi-staging and tapered leg geometry to improve its performance has not been conceived. Thus, we present a thermodynamic modeling and optimization of a two-stage thermoelectric generator (TTEG) with tapered leg geometries using ansys 2020 r2 software. The optimized parameters include the leg height, area, concentrated solar radiation, and external load resistance. First, the X-leg TEG only improves the performance of the trapezoidal leg TEG below a leg height of 3 mm. Beyond 3 mm, the performance of both TEGs become very similar. Long thermoelectric legs provide higher efficiencies, while short legs generate maximum power densities. To obtain maximum efficiencies, the initial leg height of the thermoelectric legs, 1.62 mm, is increased by 517.28%, while the initial leg area, 1.96 mm2, is decreased by 64.29%. Also, the proposed TTEG with tapered legs (trapezoidal and X-legs) improves the exergetic efficiency of the base case, single-stage rectangular leg TEG, by 16.7%. Furthermore, the use of tapered leg TEGs, in single and multi-stage arrangements, reduces the exergy conversion index of conventional rectangular leg TEGs by 1.89% and 0.98%, respectively. Finally, the use of tapered legs and multi-stage configurations increases the thermodynamic irreversibilities of conventional rectangular leg TEGs, thus reducing their thermodynamic stability.

Modeling and simulation of a hybrid system of trickle bed reactor and multistage reverse osmosis process for the removal of phenol from wastewater

Phenol is one of the most toxic and harmful pollutants in industrial wastewater streams, the removal of which is therefore of critical importance. The use of reverse osmosis (RO) systems as a means of treating wastewater is continuously growing. This research investigates the effect of operating parameters on the performance of five different multistage RO configurations coupled with a trickle bed reactor (TBR) using model-based simulation. The results were compared, and an analysis was then performed to identify which hybrid TBR and multistage RO arrangement rejected the most phenol content. The basis for comparison was four performance metrics of permeate concentration, rejection, recovery, and specific energy. The study found that the flow rate and concentration have little effect on the operation unless there is a concurrent increase of both. It was also found that the four-performance metrics used were interlinked and affect the quality and quantity of the final freshwater product.

Loss assessment of a counter rotating open rotor using URANS/LES with phase-lagged assumption (draft)

This paper presents the study of the losses generated in a Counter Rotating Open Rotor (CROR) configuration at three different operating conditions (approach, cutback and sideline). Unsteady Reynolds Averaged Navier-Stokes (URANS) and Large-Eddy Simulation (LES) approaches are used and compared to describe the flow field and the mechanisms of loss. Since no common circumferential periodicity occurs in the two blade rows of the configuration (11 blades for the front rotor and 9 for the rear rotor), a full 360∘ simulation would be required. In order to reduce the related computational cost, a phase-lagged assumption approach is used. This method enables to perform unsteady simulations on multi-stage propulsive configurations including multiple frequency flows with a computational domain reduced to one single blade passage for each row. The phase-lagged approach requires a large data storage reduced in the study by a data compression method. The data compression method is based on a Proper Orthogonal Decomposition (POD) replacing the traditional Fourier Series Decomposition (FSD). The inherent limitation of the phase-shifted periodicity assumption remains with the POD data storage but this compression method alleviates some issues associated with the FSD, especially spectrum content issues. The analysis of the losses generated in the configuration is based on an entropy formulation. In particular, the losses are split between boundary layer contributions and the remaining domain where wakes and secondary flows occur. The study shows the influence of the leading edge vortex on the suction side boundary layer transition of the front and rear rotor blades at high rotational speed (cutback and sideline). The main source of losses is associated with the suction side boundary layer over the front and rear rotor blades with a main peak of loss production at around 75% of the blade chord.