Seal Leakage Flow Research Articles

Implementation of a Reduced Order Model for rotating seal annular leakage flow inside a centrifugal pump

Sustainability and net zero emissions targets drive the importance of turbomachinery design, optimisation, and efficient operation in modern geoenergy systems. To further enable integration of advanced large-scale technologies, accurate and resource-efficient simulations of complex equipment and systems need to be completed readily. An approach to simulate internal leakage flows of centrifugal pumps is presented, an important factor that influences equipment operation efficiency.One significant challenge when internal leakage flow is investigated is achieving sufficient simulation detail in the flow regions separating rotating and stationary components where close-running clearances are present. Computational fluid dynamics (CFD) meshes typically require excessively fine resolutions of node points in these situations for accuracy. For example, the typical annular suction wear ring clearance ranges between 0.1–0.5 mm, whilst impeller diameters and other geometric properties have length scales from 600–1200 mm or even larger.A reduced order model (ROM) of an annular seal configuration was developed that allows for analytical calculation of the leakage flow by implementing user scripting in the CFD solver setup. The ROM implementation has a low symbol count and does not require any type of logic and/or recursive and iterative functionality. Thus, fine and resource-intensive meshing can be robustly eliminated and replaced by a sufficiently detailed ROM that contributes leakage flow effects to the overall simulation.Leakage flow through the suction wear ring of a high differential head (ΔH), high flow rate, double suction centrifugal pump with water as working fluid was used as a case study for ROM development. The calibrated model was verified against a commercial fluid dynamics software package and achieved a level of precision of 2.4% with σ=0.0118 in a wide operating range of 10m⩽ΔH⩽350m and fluid temperature (T) of 283.15K⩽T⩽353.15K.The leakage flow calculated by the ROM was proven to be accurate and therefore capable of accounting for a range of pressure heads, incorporating surface roughness effects and temperature variations, and adaptable for various fluids. Guidance for the implementation of the ROM in the Ansys CFX solver environment is also provided to aid future work.

Detailed Simulations of a Three-Stage Supercritical Carbon Dioxide Axial Compressor with a Focus on the Shrouded Stator Cavities Flow

This paper describes the findings of detailed simulations performed to investigate the impact of seal teeth cavity leakage flow on the aerodynamic and thermal performance of a three-stage supercritical CO2 axial compressor. The study compares a shrouded stator configuration (with cavities) to a cantilevered stator configuration (without cavities) to highlight their differences. High-fidelity computational fluid dynamics simulations were performed using non-linear harmonic (NLH) and mixing plane assumptions, considering various possible rotor/stator interface configurations for mixing plane calculations. The key performance parameters for each case were compared, and the best-performing configuration selected for further analysis. The individual stage performance parameters are also examined and compared between the cantilevered and shrouded configurations. It was observed that in the shrouded case, the leakage flow enters the cavity downstream of the stator trailing edge and gets entrained into the primary flow upstream of the stator, leading to boundary layer changes at the hub and degradation of stator and downstream rotor performance. Vortical flow structures were also observed in the stator wells, which tended to change the flow angles around the region, thereby affecting mixing and velocity distribution, resulting in a slight deterioration of compressor performance. Additionally, the study examines windage heating due to shear work from rotating walls, including the seal teeth surface. The amount of shear work done on the leakage flow and the corresponding rise in fluid temperature were quantified, tabulated, and further compared with a simple analytical model, showing good agreement between them and, hence, validating the numerical approach used.

Development of a New Loss Model for Turbomachinery Labyrinth Seals

Abstract The preliminary design of labyrinth seals requires fast and accurate estimate of the leakage flow. While the conventional bulk flow models can quickly predict labyrinth seal discharge characteristics, they lack the accuracy and pragmatism of modern computational fluid dynamics (CFD) techniques and vice-a-versa. This paper presents a new one-dimensional loss model for straight-through gas labyrinth seals that can provide quick seal leakage flow predictions with CFD-equivalent accuracy. The present seal loss model is developed using numerical experimentation technique. Multiple CFD computations are conducted on straight-through labyrinth seal geometries for a range of pressure ratios. A distinct postprocessing methodology is developed to extract the through-flow stream tube in seal. Total pressure losses and flow area variations experienced by the flow in seal stream-tube are systematically accounted for based on the well-known knife-to-knife (K2K) methodology. Regression analyses are conducted on the trends of variations of loss and area coefficients to derive the independent pressure loss and flow area correlations. These novel correlations can predict the bulk leakage flow rate, windage flow rate, and interknife static pressures over a wide range of variations of flow and geometry parameters. Validation study shows that the leakage mass flow rate predicted by this model is accurate within ±8% of measured test data. This fast and accurate model can be employed for various applications such as in seal design-analysis workflows, for secondary air system (SAS) performance analysis, and for the rotor-dynamic and aeroelastic assessments of seals.

Accurate measurement and evaluation method of axial compressor efficiency under the influence of multiple factors

Abstract In order to improve the effectiveness of compressor efficiency measurement results under the influence of complex factors, several research work have been carried out, such as inverse connection of thermocouple suitable for efficiency measurement under low pressure ratio and small temperature rise conditions, torque efficiency correction considering the mechanical loss of high speed gearbox under various working conditions, and identification of the impact of seal cavity leakage flow on efficiency measurement. Compared with the conventional connection method of thermocouple, the inverse connection method of thermocouple shows obvious advantages in efficiency measurement under low pressure ratio and small temperature rise conditions. At medium and low speeds, the conventional simplified correction method will lead to the high measurement results of torque efficiency after installing the high speed gearbox. The accuracy of torque efficiency measurement can be improved by adopting the improved correction method. Increasing the oil supply pressure of the high speed gearbox or reducing the oil supply temperature will increase the mechanical loss of the high speed gearbox. The air flow in the compressor bearing seal chamber will leak into the flow passage through the labyrinth clearance, resulting in discontinuous changes of the inlet/outlet flow of compressor.

Periodic Unsteady Kinematics of Hub Flows in a Shrouded Multistage Compressor

Abstract Periodic unsteady flow kinematics in a shrouded multistage low-speed axial compressor has been measured for the first time. Data have been acquired at the inlet and exit of a shrouded third-stage stator with a particular focus on the hub flows. The newly found features of the hub flow in a shrouded multistage compressor are different from those at the midspan or in unshrouded (i.e., cantilevered) compressors. First, the merging of the second-stage stator and third-stage rotor wakes causes positive radial migration near the rotor wake pressure surface at the hub of the third-stage stator inlet. Second, the low-momentum labyrinth seal leakage flow of the third-stage stator merges with the third-stage rotor wake to create streamwise vorticity at the third-stage stator inlet hub. Third, contrary to unshrouded stators, suction side hub corner separation in the shrouded third-stage stator reduces rotor wake stretching. Thus, velocity disturbances are attenuated less, and amplitudes of periodic fluctuations in flow angles are larger at the third-stage stator exit hub than at midspan. The positive radial migration of the rotor wake hub flow and wake stretching reduction are expected to decrease efficiency, whereas streamwise vorticity generation is expected to increase efficiency.

Effect of Rotor-stator Axial Gap on the Tip Seal Leakage Flow of a Steam Turbine

The tip leakage flow in different axial gaps is numerically investigated based on the Reynolds-Averaged Navier-Stokes equations and k-ω SST turbulent model using commercial CFD software ANSYS Fluent. The characteristics of vortexes in the flow field of tip seal and the distribution law of rotor tip leakage loss are analyzed under the change of axial gap. The results show that the flow field in the blade tip seal undergoes complex changes with the increase of axial gap. There are two opposite vortices in the seal cavity with small axial gap, namely, the large vortex in the cavity and the small vortex near the wall of the shroud. The small vortex gradually disappears with the increase of the axial gap. When the axial gap is increased to a certain value, the reverse large vortex is formed in the cavity behind the low teeth of seal, and the leakage rate increases significantly; the steam flow angle and the mixing loss also show different changes. Based on the traditional calculation formula of tip leakage rate, a more accurate calculation formula of tip leakage rate is constructed by introducing equivalent labyrinth seal teeth to consider the variation of axial gap.

Investigation of Seal Cavity Leakage Flow Effect on Multistage Axial Compressor Aerodynamic Performance with a Circumferentially Averaged Method

The seal cavity leakage flow has a considerable impact on the performance of the aeroengine, especially on the multistage compressor. Thus, a quasi-three-dimensional simulation program named CAM is developed basing on circumferentially averaged throughflow method. The program enables a rapid diagnosis for the performance degradation of multistage compressor caused by labyrinth wear. The coupling flow field between the seal cavity leakage flow and the main flow field at the root of the shrouded stator of a high-loading three-stage compressor with inlet guide vanes (IGV) was simulated by CAM and the results indicate that seal cavity leakage flow has a significant impact on the overall performance of the compressor. That is, for a 1% increase in the seal-tooth clearance-to-span ratio, the decrease in total pressure ratio was 2.6%, and the reduction in efficiency was 0.6%. Stage performance shows that the seal cavity leakage flow reduces the pressurization capacity of the current stator and the work capacity of the downstream rotor, but has little effect on the upstream blade row. Spanwise distribution of blade element performance shows that the leakage flow leads to an increased flow blockage near the hub, resulting in spanwise migration. The incidence of the stator and rear rotor then change through the entire span. The leakage flow leads to the flow blockage and migration and hence changes the incidence angle, which results in the deterioration of compressor performance.

Influence of Seal Cavity Leakage Flow on Compressor Performance Investigated with a Circumferentially Averaged Method

In order to investigate the effect of seal cavity leakage flow on a compressor’s performance and the interaction mechanism between the leakage flow and the main flow, a one-stage compressor with a cavity under the shrouded stator was numerically simulated using an inhouse circumferentially averaged through flow program. The leakage flow from the shrouded stator cavity was calculated simultaneously with main flow in an integrated manner. The results indicate that the seal cavity leakage flow has a significant impact on the overall performance of the compressor. For a leakage of 0.2% of incoming flow, the decrease in the total pressure ratio was 2% and the reduction of efficiency was 1.9 points. Spanwise distribution of the flow field variables of the shrouded stator shows that the leakage flow leads to an increased flow blockage near the hub, resulting in drop of stator performance, as well as a certain destructive effect on the flow field of the main passage.

Numerical study on sealing performance of supercritical carbon dioxide compressor dry gas seal

Aiming at the serious problem of gap leakage between the stator and rotor of the supercritical carbon dioxide compressor, the dry gas seal scheme for centrifugal compressor of small S-CO2 power system is designed in this paper. The sealing characteristics of the single-stage spiral groove dry gas seal in the S-CO2 operating environment are studied by the large-scale commercial CFD numerical analysis software ANSYS CFX. The leakage characteristics of the S-CO2 dry gas seal at different film thicknesses are obtained. The results show that the S-CO2 dry gas seal leakage flow rate increases linearly with the increase of the film thickness. The dry gas seal leakage flow rate under different film thickness is 0.04%∼0.45% of the S-CO2 compressor flow rate, which can meet the leakage requirements of the centrifugal compressor shaft end seal in the small S-CO2 power system.

Effect of a ring type barrier and rotational speed on leakage flow of gas turbine brush seal

This paper investigates the effect of inserting a ring type barrier on leakage flow of brush seals with different bristles clearances (the distance between bristle pack tip and rotor surface). The ring is placed on both upstream and downstream sides of the bristles. An axisymmetric CFD model is employed to calculate radial pressure distribution along backing plate, axial pressure variation on rotor surface, and leakage mass flow rate of the brush seal. Reynolds-Averaged-Navier-Stokes (RANS) together with non-Darcian porous medium approach is performed to solve the flow field. The accuracy and reliability of the model are evaluated through comparison of the numerical results and experimental data. The results show that inserting the ring is not effective for the brush seal with zero clearance, neither at upstream nor at downstream. In other cases, the downstream ring is considerably more effective than the upstream one, when the ring is tangent to the back of bristles. The greater the distance between the bristles and the ring, the less reduction in leakage flow. Also, the best performance is obtained for the ring height equal to clearance size. Moreover, the effect of rotor rotation on leakage flow is investigated. The results show a negligible decrease in brush seal leakage flow with increasing the rotational speed.

Numerical Investigation on Labyrinth Seal Leakage Flow and Its Effects on Aerodynamic Performance for a Multistage Centrifugal Compressor

Labyrinth seals are widely used in industrial centrifugal compressors to reduce leakage. However, no work has been conducted to numerically investigate the detailed seal leakage flow and its effects in an environment of multistage centrifugal compressor. To clarify the flow mechanism of leakage flow and the interaction mechanism between leakage and mainstream flow in multistage centrifugal compressors, the flow of the last two stages from a four-stage centrifugal compressor is studied using computational fluid dynamics (CFD) model with and without considerations of labyrinth seal leakage paths, i.e., two shroud seals, one interstage seal, and one balance piston seal. The results show that the leakage flow in shroud and hub cavities can be described as a Batchelor-type flow. The Ekman number of the cavity Batchelor flow is small and corresponds to thin boundary layers while the Rossby number is at unity order implying the importance of rotating effects. The leakage flow through the shroud, interstage, and balance piston labyrinth seals is decreased by the combined effects of throttling and diffusion flow, and has distinctive flow structures associated with the type of labyrinth seal. The influence of leakage flow on the mainstream flow can be described by suction or injection mode. The suction mode is beneficial to the improvement of mainstream flow quality while the injection mode is harmful. This work is of scientific significance to enrich the knowledge of internal fluid mechanics and of potential application value to control and design the leakage flow in real configurations of multistage centrifugal compressors.

Characterisation of turbine behaviour for an engine overspeed prediction model

This paper focuses on the characterisation of turbine overspeed behaviour to be integrated into an engine overspeed model capable of predicting the terminal speed of the high pressure turbine (HPT) in the event of a high pressure shaft failure. The engine considered in this study features a single stage HPT with a shrouded contra-rotating rotor with respect to the single stage intermediate pressure turbine (IPT). The HPT performance is characterised in terms of torque and mass flow function for a range of expansion ratios at various non-dimensional rotational speeds (NH), up to 200% of the design value. Additionally, for each HPT expansion ratio and NH, the change in capacity of the downstream IPT, for different IPT non-dimensional rotational speeds (NI), also needs to be characterised due to the extremely positive incidence angle of the flow from the upstream rotor. An automated toolkit is developed to generate these characteristic maps for both the HPT and IPT.An unlocated high pressure shaft failure will result in rearward movement of the rotor sub-assembly. This causes changes in the rotor tip and rim seal regions, and in the rim seal leakage flow properties. Therefore, in the present work, a high fidelity characterisation of turbine behaviour with the inclusion of tip and rim seals is carried out at three different displacement locations, 0 mm, 10 mm and 15 mm, to improve terminal speed estimation. Furthermore, there is a possibility of damage to the tip seal fins of the HPT rotor due to unbalance in the spool that may result in contact between the rotor aerofoil tip and the casing. Consequently, another set of characteristics are generated with damaged tip fins at each displacement location.It is observed from the characteristics that the torque of the HPT rotor decreases with increasing NH. The HPT mass flow function initially decreases and then increases with an increase in NH. The IPT mass flow function initially remains similar and then decreases with increase in NH above values of 150%. The HPT rotor torque and IPT mass flow function decrease with rearward movement of the HPT rotor sub-assembly for all values of NH. With worn tip seal fins all parameters mentioned previously are lower than in the nominal undamaged case. The high fidelity characterisation of turbines that follows the sequence of events after a shaft failure, as described in this work, can provide accurate predictions of terminal speed and thus act as a tool for testing design modifications that can result in better management and control of the over-speed event.

Estimation of Leakage Mass Flow Rate through Labyrinth Seal Using CFD Techniques

Seal design is an essential part for turbo machinery. Seal consisting of fins is placed in a gap between stationary and rotating component to minimize the leakage flow. Seal leakage flow has been considered as an inevitable loss factor that highly affects the efficiency of any machine. During operation of the equipment, thermal expansion/contraction of components take place, which causes variation of the gap between stationary and rotating component. Importance of the study is to understand the flow behavior due to variation of the gap. The variation of gap leads to change of radial clearance between fin to metal component and subsequent change of flow pattern.
 The main focus of the paper is to estimate the leakage flow through a labyrinth seal placed between rotor and casing of a typical steam turbine. Numerical techniques using 3D CFD tool are used for this purpose. Three different seal configurations are proposed in the study. The variables of the three seal configurations are radial clearance, number of fins in the flow passage and pressure drop across the seal passages.
 As an alternative methodology, an empirical correlation is formulated based on numerical simulation results for one set of radial clearance to estimate mass flow rate through the seal. In order to validate the formulated correlation, mass flow rate is determined for another set of radial clearance and compared with numerical simulation results. It is observed that flow rate estimated from 3D CFD study is around 20% lower compared to empirical correlation.

Quantifying Loss Mechanisms in Turbine Tip Shroud Cavity Flows

Numerical calculations, steady as well as unsteady, of flow in a turbine stage with a tip shroud cavity elucidate that the loss-generating flow features consist of tip seal leakage jet, the interaction of cavity exit flow with main flow, the partially recirculating cavity inlet flow interaction with vane wakes, and injection of leakage flow into the shroud cavity. The first two flow features, namely, the tip seal leakage flow and mixing of cavity exit flow with main flow, dominate while the injection of leakage flow plays an indirect role in affecting the loss generation associated with cavity exit flow. The tip shroud cavity flow essentially consists of a system of toroidal vortices, the configuration of which is set by the cavity geometry and changes when subject to unsteady vane–rotor interaction. The role which the toroidal vortices play in setting the cavity inlet recirculating flow pattern and loss generation is delineated. It is suggested that there exists a link between the inlet cavity sizing and the toroidal vortical structure. The computed results appear to indicate that the main flow path approximately perceives the presence of the tip shroud cavity as a sink–source pair; as such a flow model based on this approximation is formulated. Loss variations with tip gap height and leakage flow injection are assessed. Results show that the expected loss due to mixing has a functional dependence on the square of the difference in their velocity magnitude and swirl. The tip seal leakage jet loss scales approximately linearly with the corrected mass flow rate per unit area over the range of tip gaps investigated.

Thermal-hydraulic analysis of NSSS and containment response during extended station blackout for Maanshan PWR plant

A thermal-hydraulic analysis has been performed with respect to the response of the nuclear steam supply system (NSSS) and the containment during an extended station blackout (SBO) duration of 24h in Maanshan PWR plant. Maanshan plant is a Westinghouse three-loop PWR design with rated core thermal power of 2822MWt. The analyses in the NSSS and the containment are based on the RELAP5-3D and GOTHIC models, respectively. Important design features of the plant in response to SBO are considered in the respective models, e.g., the steam generator PORVs, turbine driven auxiliary feedwater system (TDAFWS), accumulators, reactor coolant pump (RCP) seal design, various heat structures in the containment, etc. In the analysis it is assumed that the shaft seal in each RCP failed due to loss of seal cooling and the RCS fluid flows to the containment directly. Some parameters calculated from the RELPA5-3D model are input to the containment GOTHIC model, including the RCS average temperature and the RCP seal leakage flow and enthalpy. The RCS average temperature is used to drive the sensible heat transfer to the containment. It is found that the severity of the event depends mainly on whether the secondary side is depressurized or not. If the secondary side is depressurized in time (within 1h after SBO) and the TDAFWS is available greater than 19h, then the reactor core will be covered with water throughout the SBO duration, which ensures the integrity of the reactor core. On the contrary, if the secondary side is not depressurized, then the RCS pressures will remain high in conjunction with the higher RCP seal leakage flow. The accumulators will not be available due to high RCS pressure and the reactor core will eventually become uncovered since there is no any water make-up. In the aspect of the containment response, the high-energy RCP seal leakage fluid continues flowing into the containment and heats up the containment. The containment pressure and temperature will increase to high values, respectively. There exists no clear relationship between the available TDAFWS time and the maximum containment pressure and temperature. The response of the containment temperature is much worse than that of the containment pressure. The most severe containment temperature response occurs for the case with no secondary depressurization and the calculated maximum containment temperature is 336.8°F, which exceeds the design temperature of 300°F but is still below the inside-containment safety-related equipment environmental qualification temperature of 450°F.

Principle and Application of On-line Monitoring Method for Intermediate Pressure Balance Piston Seal Clearance and Leakage Flow in Steam Turbine

Principle and Application of On-line Monitoring Method for Intermediate Pressure Balance Piston Seal Clearance and Leakage Flow in Steam Turbine

Effect of honeycomb seals on loss characteristics in shroud cavities of an axial turbine

The loss in efficiency due to shroud leakage or tip clearance flow accounts for a substantial part of the overall losses in turbomachinery. It is important to identify the leakage loss characteristics in order to optimize turbomachinery. At present, little information is available in the open literature concerning the effect of honeycomb seals on the loss characteristics in shroud cavities of an axial turbine, despite of the widespread use of the honeycomb seals. Therefore, interaction between rotor labyrinth seal leakage flow with and without honeycomb facings and main flow is investigated to provide the loss characteristics of the mixing process of the re-entering leakage flow into the main flow. The effects of honeycomb seals on the flow in shroud cavities and interaction with the main flow are analyzed. An additional study on the impact of subtle shroud cavity exit geometry is also presented. The investigation results indicate that the honeycomb seal affects the over tip leakage flow and reduces mixing losses when compared to the solid labyrinth seal. The leakage flow interactions with the main flow have considerably changed the flow fields in the endwall regions. The proposed research reveals the effects of honeycomb seals on the loss characteristics in shroud cavities and the impact of subtle shroud cavity exit geometry, and it is helpful for the design optimization of turbomachinery.

Flow Force Analysis of a Variable Force Solenoid Valve for Automatic Transmissions

Three-dimensional numerical simulations were carried out to investigate the flow dynamic behavior and pressure characteristics of a variable force solenoid (VFS) valve used in automatic transmissions. To visualize the dynamic movement of the spool, a moving mesh with dynamic layering meshes for varying boundary conditions was employed. Relevant experiment was performed to validate the simulations. The VFS valve was characterized by determining the variation in the equivalent orifice area with the spool displacement. The pressure sensitivity was found to be precisely controlled by the relation between the depth and the area of the notch in the range of the characteristic length of the valve. The results of model C, which takes into account both seal leakage and notches, indicate that there are linear pressure sensitivities in the range of the valve overlap and that there are smooth pressure control characteristics in the range of the two notches. The VFS valve with a spool was shown to have an unavoidable and unique hysteresis, which is caused by the nonlinear electromagnetic forces at the end of strokes of the spool and by the friction forces in the valve overlap. The effects of varying the oil temperature on the pressure sensitivity curves and the seal leakage flow rates were also examined.

Investigation of Three-Dimensional Unsteady Flows in a Two-Stage Shrouded Axial Turbine Using Stereoscopic PIV—Kinematics of Shroud Cavity Flow

This paper presents an experimental study of the behavior of leakage flow across shrouded turbine blades. Stereoscopic particle image velocimetry and fast response aerodynamic probe measurements have been conducted in a low-speed two-stage axial turbine with a partial shroud. The dominant flow feature within the exit cavity is the radially outward motion of the main flow into the shroud cavity. The radial migration of the main flow is induced by flow separation at the trailing edge of the shroud due to a sudden area expansion. The radially outward motion is the strongest at midpitch as a result of interactions between vortices formed within the cavity. The main flow entering the exit cavity divides into two streams. One stream moves upstream toward the adjacent seal knife and reenters the main flow stream. The other stream moves downstream due to the interaction with the thin seal leakage flow layer. Closer to the casing wall, the flow interacts with the underturned seal leakage flow and gains swirl. Eventually, axial vorticity is generated due to these complex flow interactions. This vorticity is generated by a vortex tilting mechanism and gives rise to additional secondary flow. Because of these fluid motions combined with a contoured casing wall, three layers (the seal leakage layer, cavity flow layer, and main flow) are formed downstream of the shroud cavity. This result is different from the two-layer structure, which is found downstream of conventional shroud cavities. The seal leakage jet formed through the seal clearance still exists at 25.6% axial chord downstream of the second rotor. This delay of complete dissipation of the seal leakage jet and its mixing with the cavity flow layer is due to the contoured casing wall. Time-averaged flow downstream of the shroud cavity shows the upstream stator’s influence on the cavity flow. The time-averaged main flow can be viewed as a wake flow induced by the upstream stator whose separation at the shroud trailing edge induces pitchwise non-uniformity of the cavity flow.

The impact of rotor labyrinth seal leakage flow on the loss generation in an axial turbine

This paper examines the impact of labyrinth seal leakage flow over the rotor shroud on the loss generation in an axial turbine stage. Numerical studies have been carried out with an in-house solver using the Baldwin-Lomax turbulence model to identify the changes in secondary flow structures. The code has been validated for this application using test data from a low-speed axial turbine stage with a simple generic rotor shroud labyrinth seal. Numerical simulations are carried out with different clearance gaps (0, 1, and 3 mm) and without cavity wells. The simulations are used to distinguish the separate interactions of the main flow with the leakage flow and the cavity flow. The leakage flow causes a strong increase in the secondary flow kinetic energy in the downstream stator. Both the leakage flow and the cavity flow lead to an increase in the secondary kinetic energy in the rotor.