Decrease In Pressure Ratio Research Articles

Study on Rain Absorption Performance and Flow Field of Transonic Compressor under Different Working Conditions

Taking a four-stage transonic compressor as the research object, the Lagrange particle tracking method was used to simulate the multiphase flow by considering the particle fragmentation, collision and evaporation models, and the influence of different inlet conditions (raindrop diameter, velocity, temperature and flow rate) on the compressor’s performance and stable working range was studied. The results show that inlet rain absorption can weaken the clearance leakage vortex make the shock wave move downstream, thus increasing the inlet flow rate, resulting in a decrease in stability margin and the highest efficiency point moving in the direction of flow increase. With the decrease in raindrop diameter, the pressure ratio and wet compression efficiency increase, and the stability margin decreases. With the increase in inlet raindrop velocity, the degree of pneumatic breakage increases and the raindrop diameter becomes smaller, which leads to the decrease in pressure ratio and efficiency. The influence of the mass flow rate of imported raindrops on the stable working range is significant. When the mass flow rate of imported raindrops accounts for 5% of the design flow, the stable working range can be reduced by more than half. Rain absorption increases the reaction force of the compressor and increases the load of the rotor blade.

Visualization experiment of solid-liquid two-phase flow transportation in a jet pump

Abstract Due to its lack of internal moving components, the jet pump offers widespread application possibilities in solid-liquid two-phase flow transportation. Utilizing high-speed photography, this research established a visual experimental platform for jet pumps, allowing for a detailed study and analysis of the dynamics of solid particles entering, mixing, and being conveyed through the jet pump. The following results were obtained. The introduction of solid phase particles into the jet pump results in decreased pressure ratio and efficiency, yet the general trajectory of change within the pump system remains constant. With decreasing particle size, particles become increasingly susceptible to being entrained and propelled into the jet pump by the high-velocity jet flow. The proportion of particle distribution in the mixing chamber rises as the flow ratio goes up. However, when the flow ratio falls below 0.6, the changes in particle distribution beneath the jet zone of the mixing chamber become insignificant, primarily due to the impact of particle deposition within the suction chamber. A reflux zone is observed in the throat, which gradually shrinks in length as the flow ratio increases.

Experimental and simulation study of energy loss mechanism of low pressure ratio radial turbine

Low-pressure ratio conditions are commonly encountered in radial turbines. When operating at low pressure ratio condition, a significant portion of the turbine energy loss occurs as residual velocity loss in the form of swirling flow at the outlet pipe. Typically, this energy can be recovered by the next stage turbine or reduced by the diffuser. However, there is a lack of experimental and simulation studies on the swirling flow at the outlet of turbines. The mechanism governing the changing pattern of swirling flow remains unclear, limiting the effective utilization and reduction of residual velocity loss. This study conducts theoretical and experimental research on turbine outlet swirling flow. Firstly, this paper introduces a novel two-dimensional hot-wire anemometry stepping mechanism for measuring swirling flow at a turbine outlet cross-section. Experimental results demonstrate that the proposed measurement method effectively captures the morphological changes of turbine outlet swirling flow. The results indicate a strong coupling relationship between axial and circumferential velocity. Subsequently, to elucidate the reasons for the coupling of velocity in two directions and the development of swirling flow in the outlet pipeline, simulations of turbine performance under different velocity ratio conditions were conducted. Results show that under a wide range of velocity ratios, not only does the direction of the turbine outlet swirling flow change, but it also leads to the swirl number exceeding the critical swirl ratio under high velocity ratio conditions, resulting in the formation of a central recirculation zone (CRZ) at the pipe outlet. The main cause of the strong coupling effect between velocities in two directions is attributed to the increased swirl intensity leading to enhanced adverse pressure gradients at the core of the vortex. Lastly, a model describing the variation of VGT turbine outlet swirling flow is established, indicating a linear relationship between the swirl number and the velocity ratio, with a steeper change as the pressure ratio decreases.

Research on the Combustion Mode and Thrust Performance of Rotating Detonation Scrarmjet Engines

Decades of research in hypersonic science and engineering have shown that scramjet engines are the preferred choice for powering hypersonic vehicles. In these engines, oblique shock combustion and rotating detonation combustion are two common combustion modes. This article primarily focuses on the numerical simulation and theoretical analysis of these two combustion modes. The research indicates that as the combustible mixture injected into the combustion chamber increases, the combustion mode transitions from deflagration combustion to self-sustaining detonation combustion and then to forced detonation combustion to maintain stable combustion in the chamber. Under self-sustaining detonation combustion mode, as the amount of combustible mixture injected into the chamber increases, the number of detonation waves gradually increases from one to multiple and the angle between the detonation waves and the inflow changes from acute to right angles. In the forced detonation combustion mode, the minimum shock wave intensity required to initiate detonation combustion can be obtained by drawing a tangent from the Rayleigh line. The structure generating oblique shock waves in the combustion chamber needs to match the shock wave intensity. In the detonation combustion mode, both the exit total temperature and specific impulse of the combustion chamber increase with the increase in Mach number at the inlet, while the pressure ratio decreases. This article provides a reference for the design of the combustion chamber in supersonic combustion ramjet engines.

Rotating detonation combustor performance informed through a novel megahertz-rate stagnation pressure measurement

An experimental stagnation pressure measurement technique is presented for a rotating detonation combustor (RDC). Schlieren imaging enables rotating detonation wave passage to be correlated with oscillations observed in the under-expanded exhaust plume. By measuring the spatiotemporal variation in exhaust plume divergence angle, stagnation pressure measurements of the RDC were acquired at a rate of 1 MHz. Combustor mass flux was varied between 202 and 783 kg/m2s, producing equivalent available pressures (EAPs) in the range of 3.42–13.5 bar. Time-averaged stagnation pressure measurements gathered using this technique were in agreement with the measured EAP within ±1.5%. Time-resolved stagnation pressure measurements allow for the pressure ratio produced across detonation wave cycles to be determined. For the conditions tested, detonation pressure ratios and wave speeds decreased while increasing the mean operating pressure of the combustor. Numerical modeling of the conditions tested indicates that the decrease in pressure ratio and wave speed is a result of elevated levels of combustion prior to the detonation wave arrival (i.e., “preburning”). Simultaneous OH* chemiluminescence measurements within the combustion chamber show an increase in preburned heat release relative to detonative heat release for increasing operating pressures of the RDC, in agreement with the results of the numerical model. Modeled chemical kinetic timescales decrease by approximately the same magnitude by which the preburning mass fraction increased in the range of operating pressures tested, suggesting that the faster reaction rates associated with higher pressure combustion may be the reason for increased preburning within the combustor.

Calculating Cooled Turbine Efficiency With Weighted Cooling Flow Distributions

Abstract The ability to accurately characterize the thermal efficiency of turbine stages with cooled components is essential to advance turbine technologies. There are many methods for calculating aerodynamic efficiency of turbomachinery components, with most encompassing either single point or simple integrated values at the inlet and exit locations. For cooled turbine stages, there is an added complexity of how to incorporate cooling flow streams. Although these techniques may include multiple cooling flows, a fully mixed assumption is often invoked without directly accounting for distributions of cooling flow in the annulus. However, the distribution of cooling flows in turbine stages may vary significantly depending on the location and nature of injection. This study addresses how calculated efficiency may vary depending upon how cooling flows are injected and the manner in which these cooling flows are accounted. The analyses utilize experimentally measured cooling flow concentration profiles to motivate a new approach for calculating cooled turbine efficiency with weighted cooling flow distributions. Validation data for a one-stage high-pressure turbine geometry from the energy efficient engine (E3) program are assessed to determine the range of influence for cooling flow distributions. Results show that cooling flows injected at similar axial positions can have unequal influences on integrated stage efficiency based on known distributions of cooling flow and other properties at the turbine stage exit plane. In some cases, deviations approaching half a point of efficiency can be observed relative to traditional equations, and the magnitude of influence is shown to increase as stage total pressure ratio decreases.

The comparative analysis of the R290 heat pump system working with standard expansion valve and two-phase ejector

The heat pump systems play a significant role in the global energy transition process of household heating sources towards zero-emission. One of the key technologies to improve the efficiency of heat pump systems utilizing natural working fluids is application of the two-phase ejector, which is able to recover part of the expansion losses. The comparative experimental analysis of a novel ejector-based air-source R290 heat pump was performed. The two two-phase bypass ejectors were installed in a R290 heat pump unit and a number of modifications were introduced to the baseline system. The adaptions included implementation of the internal heat exchanger, increasing the superheat at the compressor suction port, and a liquid separator for handling the two-phase flow at the ejector outlet. The performance evaluation of the system was based on COP and system heating capacity. The comparative analysis with the R290 heat pump utilizing standard expansion valve and two-phase ejector was carried out for typical operating conditions for its domestic application during heating seasons. The system working with an ejector as a throttling device allowed for up to 33% of COP improvement over the system utilizing an expansion valve. Additionally, the ejector implementation resulted in decreased pressure ratio of the compressor, which increased the system heating capacity by up to 90%.

Local momentum flux measurement: An effective way for GDI spray targeting in flash boiling conditions

Fuel injection and spray development are crucial processes for gasoline direct injected engines as an extremely accurate control of mixture formation is mandatory in order to attain high thermal efficiency targets while limiting pollutant emissions formation (mainly soot and NOx). In particular detecting the actual spray targeting is challenging as the spray evolution is significantly affected by the wide range of injection operating conditions typically implemented in GDI engines to allow a proper combustion process control. Peculiar injection strategies (rail pressure level, number of injection events) and combustion chamber pressure/temperature levels can result in flash boiling conditions, in which both the atomization process is enhanced and the spray structure is heavily modified with respect to the nominal one, with the different jets possibly collapsing in one single plume. The spray structure experimental analysis is problematic in flash boiling conditions, being conventional optical techniques as imaging and phase Doppler anemometry often unable to provide quantitative data about the inner spray structure, particularly very close to the nozzle. In this study, the actual spray evolution in flashing and non-flashing conditions was investigated by imaging and by momentum local distribution measurement, a methodology based on the spray-impact force method applied to small portions of the fluid structure to detect the local contribution of both the liquid and the gaseous phases to the jet momentum flux. The resulting momentum flux maps can be obtained very close to the nozzle and are not affected by the injector and test chamber operating conditions, offering a significant insight in the jet-to-jet interaction and spray evolution in flash boiling conditions. The obtained results evidenced the progressive modification of the spray structure of a 6-hole symmetrical GDI nozzle from standard to flare flash-boiling conditions, passing from transitional state. The plumes fingerprint gets larger when the ambient to saturation pressure ratio decreases and, when flare flash-boiling occurs, the plumes interaction becomes so intense that the spray structure collapses with a strong reduction of the global cone angle and an increased tip penetration. The obtained results confirmed momentum distribution maps to be an effective way to quantitatively analyze the actual spray targeting, the hole-to-hole flow distribution and the overall spray evolution under a wide range of operating conditions, overcoming severe limitations of other diagnostics like spray visualization and phase Doppler anemometry.

Design of a Supercritical CO2 Compressor for Use in a 1 MWe Power Cycle.

Supercritical CO2 power cycles are considered to be a more effective means to replace the steam Rankine cycle in power generation by power coal in the future. However, CO2 compressors for this application have not been well developed. A conceptual design of the compressor for a 1 MWe cycle has been summarized and a calculation method of the axial force of a supercritical CO2 compressor has been introduced. The influences of inlet temperature and pressure near the critical point on compressor performance, the rotor dynamics analysis for this compressor, and the influence of the rotation factor C0 on compressor axial force were also investigated. The results show that the changes in inlet temperature and pressure near the critical point have great influences on compressor performance and the axial force of the compressor is closely related to the selection of the rotation factor C0. The pressure ratio and power decrease with the increase of inlet temperature; when the inlet temperature increases by 2 °C, the pressure ratio decreases by 7–24% and the power decreases by 1–9%. With the increase of inlet temperature, the maximum efficiency of the compressor decreases, and the maximum pressure ratio of the compressor decreases with the increase of inlet pressure. When the rotation factor C0 is equal to 0 and 0.2, the axial force of the compressor decreases with the increase of rotating speed. When the rotation factor C0 is equal to 0.4, the curves of the compressor with the flow rate at different speeds begin to produce intersections. When the rotation factor C0 is equal to 0.6, 0.8, and 1, the axial force of the compressor increases with the increase of rotating speed.

Numerical optimisation of a micro-wave rotor turbine using a quasi-two-dimensional CFD model and a hybrid algorithm

Wave rotors are unsteady flow machines that exchange energy through pressure waves. This has the potential for enhancing efficiency over a wide spectrum of applications, ranging from gas turbine topping cycles to pressure-gain combustors. This paper introduces an aerodynamic shape optimisation of a power generating non-axial micro-wave rotor turbine and seeks to enhance the shaft power output while preserving the wave rotor’s capacity to function as a pressure-exchanging device. The optimisation considers six parameters including rotor shape profile, wall thickness, and number of channels and is done using a hybrid genetic algorithm that couples an evolutionary algorithm with a surrogate model. The underlying numerical model is based on a transient, reduced-order, quasi-two dimensional computational fluid dynamics model at a fixed operating condition. The numerical results from the quasi-two-dimensional optimisation indicate that the best candidate design increases shaft power by a factor of 1.78 and imply a trade-off relationship between torque generation and pressure exchange capabilities. Further evaluation of the optimised design using three-dimensional computational fluid dynamics simulations confirms the increase in power output at the cost of increased entropy production. It is further disclosed that increased incidence losses during the initial opening of the channel to the high-pressure inlet duct compromise the shock strength of the primary shock wave and account for the decrease in pressure ratio. Finally, the numerical trends are validated using experimental data.

Optimisation of the fuelling of hydrogen vehicles using cascade systems and ejectors

The present study investigates the replacement of expansion valves, used in the cascade system of hydrogen fuelling stations, by a series of ejectors. The major advantage of using ejectors is to recover part of the kinetic energy lost during the expansion of a high-pressure primary flow, in order to entrain a lower pressure secondary flow; thus resulting in a more efficient fuelling.Firstly, a quasi-steady 1-D simulation model of the ejector was calibrated using computational fluid dynamics in terms of the main geometry and pressure conditions.Secondly, the quasi-steady 1-D model of the ejector was used in a dynamic model of the hydrogen fuelling station, in order to investigate the influence of its geometry on the transient fuelling performances. Different fuelling scenarios were explored with varying number of buffer tanks in the cascade system of the fuelling station, and different initial pressures in the vehicle's tank. The results show that the replacement of the expansion valve by an ejector may reduce the energy consumption for hydrogen compression by up to 6.5% using two buffer tanks in the cascade system. On the other hand, increasing the number of buffer tanks reduces the energy savings as the driving pressure ratio decreases.

A new unsteady casing treatment for micro centrifugal compressors to enlarge stall margin

Tip clearance flow, particularly tip leakage vortex, is an important source of losses in centrifugal compressor rotors, which limits the stall margin and even causes compressor surge. To address this issue, a passive unsteady flow control method is proposed with equal-circumferential-spacing through-holes on the casing of a micro centrifugal compressor. The numerical simulation shows that the unsteady excitation near the generating position of the leakage vortex can weaken the fluctuation caused by the leakage vortex. The stall margin increases by 19.3% and the efficiency decreases by 0.8% when the mass flow rate of the excitation flow is only 0.12% of the main flow. Furthermore, a proof experiment on a micro centrifugal compressor shows that the stall margin increases by 13.3% considering a 100% design rotation speed and 15.4% considering an 80% design rotation speed, while the efficiency and pressure ratio decrease slightly. Therefore, both the simulation and experiment prove that the flow control method is effective and can easily be used in practice.

Experimental investigation on working fluid selection in a micro pulsating heat pipe

A guideline for the working fluid selection in a micro pulsating heat pipe (MPHP) is experimentally developed. A closed-loop ten-turn MPHP with overall dimensions of 80×35×1.7 mm3 is fabricated using MEMS manufacturing process. Ethanol, FC-72, HFE-7000, R-245fa, and R-134a are selected for the working fluids. The filling ratio of the working fluids is fixed to be 50% at room temperature. The thermal resistance of the MPHP is evaluated and the flow is visualized with a high-speed camera in a vertical orientation. It is found that the thermal resistance of the MPHP reduces as the condenser temperature rises or the working fluid changes in the following order: ethanol, FC-72, HFE-7000, R-245fa and R-134a. The decrease of the thermal resistance is due to the enhanced latent heat transfer resulting from the increase of the average volumetric fraction in the condenser section. Based on these experimental findings, the average volumetric fraction in the condenser section is assumed to be related to the driving pressure for the fluid motion and the frictional pressure drop. Then, it is postulated that the figure of merit for the working fluid selection is proportional to the ratio of the driving pressure for the fluid motion to the frictional pressure drop. This postulate is consistent with the experimental findings, which demonstrated that the thermal resistance of the MPHP decreases as the inverse of the pressure ratio decreases. Finally, the figure of merit, which can be used to select a working fluid for the minimum thermal resistance of a PHP as reported in the present study and in other studies, is proposed.

Investigation Into the Phenomenon of Flow Deviation in the S-Shaped Discharge Passage of a Slanted Axial-Flow Pumping System

Abstract A remarkable flow deviation phenomenon exists in the S-shaped discharge passage of a slanted axial-flow pumping system. In order to reveal the characteristics and development process of the deviating flow, numerical simulation was performed for a 15 deg slanted axial-flow pumping system, and the deviating flow was measured on an experimental rig. The details of the deviating flow in the S-shaped discharge passage were obtained. A kind of “unwinding” flow structure similar to that of DNA in biology is found in the S-shaped passage. The special structure is characterized by a “single strand” in which original helical streamlines are almost straightened. The bulk speed of the fluids on the “single strand” on the left side of the passage significantly increases while the swirling strength and the kinetic pressure ratio decrease. Large-scale Dean vortices at the passage bottom interact with high transverse energy gradient fluids at the passage top as water flows into the convex part of the S-shaped passage, which leads to the emergence of the “unwinding” structure. Reverse secondary flows further enlarge the scale of the Dean vortices as water flows into the concave part of the S-shaped passage, which results in the growth of the “unwinding” structure. With the development of the asymmetrical flow structure, an irreversible severe flow deviation problem naturally comes into being.

Hydrogen decompression analysis by multi-stage Tesla valves for hydrogen fuel cell

Abstract Hydrogen fuel cell is an ideal power source for electric vehicles. For a hydrogen fuel cell electric vehicle, the hydrogen is reserved in a high pressure level to promote the recharge mileage while relatively low-pressure hydrogen is demanded for proper functioning of the fuel cell stack, so that decompression of hydrogen is needed before hydrogen flowing into the fuel cell. With a reverse flow through Tesla valves, there appears a large pressure drop between the inlet and outlet, which can be used for hydrogen decompression nicely. However, a single-stage Tesla valve cannot meet the pressure drop requirement, so multi-stage Tesla valves are utilized. In this paper, numerical simulations of reversed hydrogen flow through multi-stage Tesla valves are carried out. The stage number of multi-stage Tesla valves and the inlet/outlet pressure ratio are both studied, and the distributions of temperature, pressure, and velocity inside multi-stage Tesla valves are all investigated. Results show that as the stage number increases or the inlet/outlet pressure ratio decreases, the pressure and the velocity inside multi-stage Tesla valves decrease, and the less the stage number, the more possibility for the velocity higher than local acoustic speed. Besides, a power-law relationship between the flow rate, the stage number and pressure ratio is summarized.

Dehydration of low-pressure gas using supersonic separation: Experimental investigation and CFD analysis

Supersonic nozzles are recently applied for carrying out water separation from natural gas streams and dew pointing in early stages of gas processing. This paper represents an experimentally and numerically study on a novel low-pressure two-phase driven supersonic nozzle constructed based on a new annular design. The nozzle includes a set of tilted fixed blades at the entrance and a swirling stabilizer along with a convergence-divergence nozzle. The liquid phase is separated from the primary gas phase by decompression and compression happening accompanied with the centrifugal effect induced by the swirling of the gas stream. The phase change happens by gradual drops in temperature and pressure upstream of the shockwave position, and an abrupt change at the shockwave position followed by a subsequent gradual increase in temperature and pressure. The pressure, temperature, and moisture level of the gas are measured to investigate the performance of the supersonic separation unit.The computation is carried out by a 2D approach capable of two-phase heat and mass transfer modeling. For the first time, the analysis uses high order of discretization schemes in order to well capture the shockwaves in a low-pressure supersonic nozzle and find out their effects on separation. An assessment is carried out focusing on the effect of operational conditions on the nozzle performance. The experimental data for dehydration efficiencies are in good agreement with the simulation results within 3%.The shockwave position is found in the range of 0.3–0.5 of non-dimensional nozzle length. The positions of both shockwave and initiation of condensation are shifted toward the exit side when the nozzle pressure ratio decreases. Reducing the pressure ratio from 0.8 to 0.6 will enhance the dehydration efficiency by about 5%.

Design and performance analysis of three stage centrifugal turbine

In this paper, the three-stage centrifugal turbine was designed based on the thermodynamic parameters of a four-stage test axial turbine. 1D aerodynamic design, 3D numerical simulation and optimization, and analysis on off-design performance of the centrifugal turbine were conducted. The results show that the key simulation parameters including total-static efficiency, shaft power, reaction degree, velocity ratio and pressure ratio of turbine stages are close to the 1D calculation values; at the design condition, streamline is smooth in the passage of turbine cascades; high efficiency has been obtained, indicating that the aerodynamic performance of three-stage centrifugal turbine meets the designed requirements. In off-design condition, the total-static efficiency of the designed turbine increases with the increase of pressure ratio first and then decreases; the shaft power decreases with the increase of pressure ratio; the mass flow rate increases gradually with the decrease of pressure ratio and finally tends to be constant when the turbine is under the blocking condition; the variation trend of total-static efficiency, shaft power, mass flow rate with the pressure ratio is similar at different speeds. The total-static efficiency, shaft power and mass flow rate of centrifugal turbine are almost equal to those of the axial turbine at design condition. The total-static efficiency of radial outflow turbine is close to that of axial flow turbine at different pressure ratio, but the mass flow rate of centrifugal turbine is smaller than that of axial flow turbine.

Multilevel optimization of profile of splitter blades in the impeller of a centrifugal compressor

In this research a multilevel optimization on the profile of splitter blades of a turbocharger compressor is performed using genetic algorithm in order to improve its performance. Successive corrections of profile at hub, midspan and shroud of splitter blades, with the objective of decreasing incidence losses at the leading edge and adjustment of blade loading at shroud, results in an impeller having improved splitter blades. The impeller flow filed analysis shows the optimization has been successful in reducing flow leakage at the shroud region and as well as losses in leading edge region. Although numerical simulations predict0.5% decrease in pressure ratio at design point, but 2.2 points improvement in isentropic efficiency is calculated. Based on the optimization results a new impeller is designed and manufactured and tested on a turbocharger test bed. Experimental results approve the simulation prediction results on the expected improvement in performance

Enhanced performance of wet compression-resorption heat pumps by using NH3-CO2-H2O as working fluid

Upgrading waste heat by compression resorption heat pumps (CRHP) has the potential to make a strong impact in industry. The efficiency of CRHP can be further improved by using alternative working fluids. In this work, the addition of carbon dioxide to aqueous ammonia solutions for application in CRHP is investigated. The previously published thermodynamic models for the ternary mixture are evaluated by comparing their results with experimental thermodynamic data, and checking their advantages and disadvantages. Then the models are used to investigate the impact of adding CO2 to NH3-H2O in wet compression resorption heat pump applications. For an application where a waste stream is heated from 60 to 105 °C, a COP increase of up to 5% can be attained by adding CO2 to the ammonia-water mixture, without any risk of salt formation. Additional advantages of adding CO2 to the ammonia-water mixture in that case are decreased pressure ratio, as well as an increase in the lower pressure level. When practical pressure restrictions are considered the benefits of the added CO2 become even larger or around 25% increase in the COP. Nonetheless, when the waste stream was considered to be additionally cooled down, no significant benefits were observed.

Observations of the Growth and Decay of Stall Cells during Stall and Surge in an Axial Compressor

This research investigated unsteady events such as stall inception, stall-cell development, and surge. Stall is characterized by a decrease in overall pressure rise and nonaxisymmetric throughflow. Compressor stall can lead to surge which is characterized by quasi-axisymmetric fluctuations in mass flow and pressure. Unsteady measurements of the flow field around the compressor rotor are examined. During the stall inception process, initial disturbances were found within the rotor passage near the tip region. As the stall cell develops, blade lift and pressure ratio decrease within the stall cell and increase ahead of the stall cell. The stall inception event, stall-cell development, and stall recovery event were found to be nearly identical for stable rotating stall and surge cases. As the stall cell grows, the leading edge of the cell will rotate at a higher rate than the trailing edge in the rotor frame. The opposite occurs during stall recovery. The trailing edge of the stall cell will rotate at the approximate speed as the fully developed stall cell, while the leading edge decreases in rotational speed in the rotor frame.