# Numerical investigations of a low-pressure turbine purge flow control concept for reducing aerodynamic losses

Jean-Hugues Beaux, Julian Girardeau, Sofiane Khelladi, Michael Deligant, Christelle Périlhon

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Jean-Hugues Beaux, Julian Girardeau, Sofiane Khelladi, Michael Deligant, Christelle Périlhon. Numerical investigations of a low-pressure turbine purge flow control concept for reducing aerodynamic losses. GPPS Chania24. Technical Conference for Power and Propulsion Sector, Global Power and Propulsion Society, Sep 2024, Crète, Greece. hal-04889104

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# NUMERICAL INVESTIGATIONS OF A LOW-PRESSURE TURBINE PURGE FLOW CONTROL CONCEPT FOR REDUCING AERODYNAMIC LOSSES

Jean-Hugues Beaux

Arts et Métiers Institute of Technology, CNAM,
LIFSE, HESAM University

jean-hugues.beaux@ensam.eu

Paris, France

Julian Girardeau

Safran Aircraft Engines

julian.girardeau@safrangroup.com

Moissy-Cramayel, France

Sofiane Khelladi

Arts et Métiers Institute of
Technology, CNAM, LIFSE,
HESAM University

sofiane.khelladi@ensam.eu

Paris, France

Michael Deligant

Arts et Métiers Institute of
Technology, CNAM, LIFSE,
HESAM University

michael.deligant@ensam.eu

Paris, France

Christelle Perilhon

Arts et Métiers Institute of
Technology, CNAM, LIFSE,
HESAM University

christelle.perilhon@lecnam.net

Paris, France

## ABSTRACT

Interaction between purge flows and main flow path is known to impact negatively the aerodynamic performance of the gas turbines. This paper focuses on the leakage flow through hub cavity re-entering into the main flow path upstream of the second rotor blade row of a two-stage low-pressure turbine (LPT). The stator well considered in this paper consists of second stator vane upstream and downstream cavities connected with a labyrinth seal mounted on an annular seal carrier. A device to reduce the mixing and subsequent row losses is numerically evaluated by assessing its impact on the turbine efficiency, as well as on the radial distribution of relevant characteristic quantities (circumferential velocity, flow angle, turbulent kinetic energy...). The feature is located underneath the nozzle guide vane endwall and a significant part of the leakage flow is passing through it, before mixing with the other part of the leakage flow and re-entering into the main flow. This paper presents numerical results of unsteady 3D simulations of a two-stage axial turbine with the turning device located upstream of the second rotor blade row. Results of three configurations are compared: the two-stage axial turbine including its inner cavity without, and then with the device and finally, the former associated to a modified nozzle guide vane platform. An increase of the turbine efficiency of 0.114% can be noticed in the best case. The turning feature reduces mixing losses between the two leakage flows before entering into the main flow path and then improve the efficiency of the subsequent row.

## INTRODUCTION

Ongoing research to improve the efficiency of gas turbines has led to significant efforts to reduce purge flow losses. Interaction between turbine rim seal purge flow and main flow path is known to impact negatively the aerodynamic performance of the gas turbines and has been the subject of numerous studies. The main contributors of these losses are the mixing losses which are driven by the momentum difference and flow direction (Denton 1993). Gier et al. (2003) presented a loss decomposition on a three-stage low-pressure axial turbine and concluded that mixing losses account for about 50% of the cavity losses.

A significant amount of studies focusing on the impact of the purge flow on the main flow aerodynamics can be found.

Based on an experimental study performed in a two-stage axial turbine, Hunter et al (2000) showed that the low momentum purge flow interacts strongly with the main annulus, as it is entrained into the rotor passage vortex and transported to the subsequent stator vane. The authors exposed that the main source of losses associated with the cavity is the low circumferential velocity of the purge flow compared to the main flow. McLean et al. (2001) used different cooling configuration (radial, impingement and root injection) and found that the pressure distribution of the main annulus is impacted by the purge flow. The interaction between purge flow and secondary flow structures before a rotor row was also
highlighted by Schuepbach et al. (2010), who determined that the hub secondary structures have a larger radial extent and measured a turbine efficiency reduction of 0.6% with the increase of purge flow rate. Similar findings have been published by Jenny et al. (2013) and Ong et al. (2012) on a low and high pressure turbine, respectively. Schrewe et al. (2011) performed similar study but with a purge flow located upstream of the second stator of a two-stage turbine. They found that an increasing rim seal mass flow leads to an intensification of secondary flow structures and greater losses across the stator.

Then, many papers highlighted the strong impact of the circumferential velocity on the purge flow losses. Zlatinov et al. (2012) quantified with a numerical study the different type of shroud and hub purge flow losses, showing that by 1.5% of leakage flow rate at the hub, turbine losses is increased by 12%. The authors identified the purge flow rate to be the parameter with the highest leverage of losses. This study also highlighted the purge flow swirl velocity as a key factor to reduce losses by 40-70%. Likewise, Ong et al. (2012) measured a stage efficiency increase of 0.75% with an increase of purge swirl angle from 0 to 70 deg. A quantitative study of losses showed that 0.4% of stage efficiency gain was due to viscous dissipation reduction and 0.35% due to a reduction of secondary structures strength. Girgis et al. (2002) presented that the disk cooling flow could be optimized to improve turbine efficiency by using tangential injection as opposed to radial injection. Finally, Reid et al. (2006) have shown experimentally and numerically that the sealant flow alter the circumferential velocity of the main flow and therefore increasing the swirl velocity of the purge flow rate has a beneficial effect on the mixing losses.

As highlighted by these numerous studies, it seems that the purge flow rate as well as its swirl velocity are the main levers for reducing the mixing losses. Working on the purge flow rate requires a special focus on the seal geometry in the hub cavity, which is not the scope of this study. As this paper aims to reduce the mixing losses in the rim seal region, a turning device was identified to extend the idea of improving the low circumferential velocity of leakage flow.

A number of numerical and experimental studies have been carried out aimed at reducing the outer cavity mixing losses using special features like the studies performed by Wallis et al. (2000) and Rosic et al. (2006).

About inner cavities, Schädler et al. (2017) performed an experimental study with features located underneath the stator and rotor platform of a high-pressure turbine. They have shown an increase in stage efficiency between 0.35 and 0.39% for two rim seal purge flow rate, by increasing the circumferential velocity of the purge flow. Similar findings was found by Mahle (2010) with turning device situated close to the rear openings of the cavities underneath the stator vane 2 and 3 on a three-stage low pressure turbine. An increase in efficiency of the turbine of about 0.1% was numerically noticed.

In contrast to prior investigations, the purge flow studied in this paper is a mixture of two leakage flows and the turning device aims to reduce the mixing losses between them, before re-entering into the mainflow path.

The first part of this paper is dedicated to a geometrical description of the turbine under investigation with a special attention being paid to the three test cases. Important aspects of the numerical simulations are also presented in this part. The next section is about the influence of the turning device on the overall performance of the turbine as well as on the different areas of the turbine. In particular, the flow field and relevant quantities in the rim seal region and in the subsequent rotor row are investigated to understand the behavior of the features.

# METHODOLOGY

The CFD modelling used to investigate the device performance is detailed in this part. The geometry as well as the mesh and the solver set-up are described. The study has been performed with the CFD solver ANSYS Fluent.

# CFD Domain

In the framework of the main annulus gas path interactions (MAGPI) program, a two-stage axial turbine test rig has been developed with the aim of providing an experimental database to further advance in the understanding of cooling flow and annulus gas interactions and resultant heat transfer in the cavities. The turbine under investigation in this CFD study is the MAGPI WP1 turbine, rated at 400 kW with a pressure ratio of approximately 2.7 at the design point speed of 10630 rpm. Each turbine stage counts 39 stator vane and 78 rotor blades to suit a simulation using a periodic sector model. Thus, the 3D CFD domain, displayed in Fig. 1a is a 1/39th sector part of the full test rig containing one stator vane and two rotor blades for each stage. Rotating and static walls are coloured in red and blue respectively. The inner cavity is located below the stator vane of the second stage and was modified compared to the initial MAGPI turbine stator well. It contains an upstream and downstream cavities connected with a labyrinth seal mounted on an annular seal carrier. Details about the turbine stator well without any device and a schematic representation of the flow are depicted in the figure 1b. One may notice that, compared to the actual MAGPI configuration, the second rotor wing has been adjusted for the needs of this study. A portion of the inlet cooling mass flow rate supplied in the cavity is ejected through the rim seal upstream of the stator 2, as the performance of the turning device is assessed in a configuration without ingress into the cavity. The cooling flow divides into two parts, one crossing the labyrinth seal and the other along the U shaped annular seal carrier clearance. At the exit of the seal carrier, the former flow may pass through the turning device (TD). Regarding the labyrinth seal mass flow, it is mostly exhausted into/across the second disk via the imposed outlet mass flow rate. The remaining of the labyrinth seal mass flow rate is mixed with the seal carrier flow, before exiting the cavity upstream of the main flowpath second
rotor row. Overall, the second nozzle aft purge mass flow rate is a mixing constituted of part of the labyrinth seal leakage and the seal carrier leakage.

<figure><img src="image_2.png" /><figcaption>Figure 1: CFD domain - Main annulus with hub cavity (a) and details of the hub cavity geometry with schematic visualisation of the flow (b)</figcaption></figure>

In this paper, three configurations have been studied:

- The first one named as baseline case (BSL), with no turning device into the cavity (Fig. 2a)

- The second one named as Turning Device (TD), with the features added into the cavity (Fig. 2b)

- The third one named as Turning Device with Modified Platform (TD-P), with the features and a modified stator vane platform (Fig. 2c)

<figure><img src="image_3.png" /><figcaption>Figure 2: Geometrical configurations with BSL (a), TD (b) and TD-P (c)</figcaption></figure>

The turning device consists of guide vanes and an annular endwall located underneath. The endwall forms a channel which confines the fluid and avoids a recirculation zone around the deflectors. The optimization of the turning device was performed with a reduced CFD domain. The height, chord length, pitch, axial position, incidence angle and deviation angle of the deflectors have been optimized to achieve the best compromise between outlet Mach number, tangential velocity and mass flow rate. In the configuration TD-P, the turning device is associated with a modified stator vane platform. The expected effect of this platform modification is an alteration of the radial and axial velocity of the seal carrier flow in order to improve the alignment of the two leakage flows before re-entering into the main flowpath.

The main annulus is set (in accordance with the MAGPI test rig) with uniform total pressure (2.8.10⁵Pa) and temperature (439K) at the inlet and with a radial equilibrium static pressure (1,13.10⁵Pa) at the outlet. The inlet and outlet of the main gas path are placed as far as possible from the stator well. The in- and outlets in the hub cavity use a fixed mass flow rate (1.25% of the main flow rate) and, for the cooling supply, a given total temperature (328K). The imposed outlet mass flows and leakage clearances have been set up to ensure that a significant part of the purge flow passes through the turning device without drifting too far away from what an actual engine configuration would be. A flow rate assessment over the whole domain is presented in Fig 4 in the results section, for the three configurations.

## Mesh Generation

The mesh was generated with ANSYS Fluent Meshing and is an unstructured polyhedral mesh. It counts 31.5M of cells for the reference case, 37.1M for the turning device case and 37.4M for the platform case. All the meshes have a growth rate of 1.07 to ensure a sufficiently low numerical dissipation. Local refinements have been added in the areas of
interest, like the rim seal purge flow as well as the trailing edge wakes of the blades. Figure 3 shows the surface mesh of the main annulus (second stage) (a) and the local refinement at the trailing edge of the turning device (b).

<figure><img src="image_4.png" /><figcaption>Figure 3: Main annulus mesh (a) and deflectors mesh in the TD configuration (b)</figcaption></figure>

The boundary layer was fully resolved over the whole domain with $y^+$ smaller than one in the areas of interest. Several criteria were satisfied for the three meshes:

- Orthogonal quality greater than 0.15

- 12 layers of polyprisms in the boundary layers

- A polyprisms aspect ratio lower than 350

## Solver set-up

As the interaction between the purge flow and the main annulus flow is expected to be unsteady, URANS simulations were carried out. All the unsteady calculations were initialized with RANS simulations. The necessity of the URANS simulations was confirmed, as high fluctuations of the relevant quantities in the rim seal area occurred along each iteration of those RANS calculations. A sliding mesh method in association with frame motion were adopted to transfer the flow information between the static and moving part through all the mesh interfaces.

These interfaces are placed in such a way that the hub cavity and rotor row of each stage are joined in the same moving domain. Thus, the interface between the stator vane and the blade row of the second stage is placed upstream of the purge/main flowpath mixing. URANS equations were solved using a second order finite volume discretization with compressible flow and viscous work. Turbulence was modelled using the $k-\omega$ SST with near wall resolved boundary layer. The Kato-Launder correction was added to limit the turbulence production at stagnation points. A bounded second order implicit method was used for the time discretization.

To ensure sufficient temporal resolution, 40 time steps per blade renewal have been chosen for a total of 3120 time steps per rotor revolution with 10 sub-iterations per time step. It was verified that the time step is small enough to ensure convergence of all the relevant quantities within 10 sub-iterations. Prior to data acquisition, two rotor revolutions have been performed. All numerical results shown in this study are time-averaged results, which were averaged over one rotor revolution. The variables with a dynamic component are post-processed by mass-weighted averaging whereas the others variables are area-weighted averaged.

## RESULTS AND DISCUSSION

In this part, the impact of the turning device in both configurations (TD and TD-P) will be studied, on the overall performance of the two-stage turbine, as well as on the relevant quantities like the relative circumferential velocity and the turbulent kinetic energy in the purge flow and at the second rotor row inlet.

### Overall turbine performance

The overall performance of the turbine is assessed with the polytropic efficiency, defined as follow:
$$n_p = \frac{\omega * M_{shaft}}{\dot{m} * \left[ \frac{k}{k-1} r * (T_{s1} - T_{s2}) + \frac{V_1^2 - V_2^2}{2} \right]} \quad \text{with } k = \frac{1}{\frac{\ln \frac{T_{s2}}{T_{s1}}}{\ln \frac{P_{s1}}{P_{s2}}} + 1} \quad (1)$$

The time-averaged torque $M_{shaft}$ is the sum of the pressure and viscous torques applied on all the rotating walls of the domain. Index 1 and 2 stand for inlet and outlet respectively. Since there are multiple in- and outlets, the quantities used in the efficiency definition are weighted by their flow rates.

With the turning device only, it was found an increase of the overall efficiency of 0.079% against the baseline case whereas the TD-P configuration allows for a 0.114% improvement in efficiency against the baseline. The efficiencies are resumed in Table 1.

<table><caption>Table 1: Overall polytropic efficiencies for each configuration</caption><thead><tr><th>BSL case</th><th>TD case</th><th>TD-P case</th></tr></thead><tbody><tr><td>92.750%</td><td>92.823%<br>+ 0.079%</td><td>92.856%<br>+0.114%</td></tr></tbody></table>

Figure 4 shows the flow distribution with streamlines and contour over the whole turbine stator well coloured by tangential velocity, for the baseline case. Figure 4 also shows a flow rate assessment over the whole domain for the three cases. Mass flow rates are time averaged and expressed as a percentage of the main annulus flow rate. The values for the BSL, TD and TD-P cases are displayed in the top, middle and bottom boxes of the tables. As expected, the cooling flow in the upstream cavity is divided into three parts. As the cavity is fully purged for this study, a small part of the cooling is ejected to the main gas path upstream of the second nozzle guide vane (1). The remaining flow is then split into two paths, one for the seal carrier clearance (2) and the other for the labyrinth seal (3). A part of the labyrinth mass flow is then ejected so that a significant part of the purge flow exiting the hub cavity upstream of the second rotor row (4) passes through the turning device. The same boundary conditions have been applied for the three cases. Since the main annulus mass flow rate remains constant between the configurations (less than 0.02% differences between the three cases), the increase of the overall turbine efficiency can be attributed to the turning device only, and is not a consequence of an off-design drift between the cases. Moreover, the flow rate assessment shows only insignificant deviations between the configurations so it is expected that the increase of overall performance is not affected by a mass flow rate variation.

<figure><img src="image_5.png" /><figcaption>Figure 4: Flow distribution for the baseline case illustrating the different flow paths and time averaged flow rate for the three configurations</figcaption></figure>
As the impact of the turning device is negligible on the inlet mass flow rate, it is expected that the first stage is also not disturbed by the features. This was confirmed by radial profiles of relative flow yaw angle β and turbulent kinetic energy (TKE) at the rotor 1 exit, displayed in Fig.5, which show that the features have no impact on the first stage operation. The relative flow yaw angle is defined as follow:

$$ \beta = \arctan\left(\frac{W_{\theta}}{V_{x}}\right) \quad (2) $$

<figure><img src="image_6.png" /><figcaption>Figure 5: Mass- and circumferentially averaged profiles of turbulent kinetic energy (a) and relative flow yaw angle (b) at the rotor 1 exit</figcaption></figure>

Only minor variations have been noticed on the second stage stator vane performance, and could be attributed to the slight variations of the mass flow rate at the rim seal upstream of the stator 2. This confirms that the increase in overall turbine efficiency is due solely to the effect of the turning device on the second rotor row.

## Rim seal flow field

To understand how the device increases the overall performance of the two-stage turbine, the time-averaged flow field at the rim seal is investigated.

In figure 6, contours of the time-averaged circumferential velocity are presented as well as the mass- and circumferentially averaged profiles for the three cases. The flow structure is also schematically depicted. As expected, it can be noticed that the flow coming from the seal carrier clearance has a low circumferential velocity (10m.s⁻¹), as it flowing along static parts.

In the baseline case (Fig. 6a), a fraction of the labyrinth mass flow recirculates above the static angel wing (red arrow labelled as “l-2”) and mixes with the seal carrier flow (green arrow labelled as “s-1”) at the exit of the seal carrier clearance. This recirculating flow is slowed down as it goes along static parts and mixes with the low circumferential velocity seal carrier flow. Thus, at the mixing area (marked by (1) on the figure) between the seal carrier and the labyrinth flows, the difference between the circumferential velocity of the two flows is considerable.

In the other configurations with the turning device (TD and TD-P), the flow structure is modified and the labyrinth flow is confined near the rotor angel wing. The increase in relative circumferential velocity of the seal carrier flow with the deflectors is noticeable at location (2). Therefore, as expected with the turning device, the velocity gradient between the labyrinth and the seal carrier flows has been reduced.

Looking at the rim seal exit, Figure 6b shows that the relative circumferential velocity remains constant with the TD geometry and is reduced with the TD-P configuration. Indeed, due to viscous effects, the labyrinth flow is centrifuged by the moving wall of the rotor and its circumferential velocity is higher than the seal carrier flow. The turning device allows the circumferential velocity of the seal carrier to increase, but it remains lower than the circumferential velocity of the labyrinth flow. To summarize, in this configuration, it is not intended to bring the seal carrier flow to the same circumferential velocity as the labyrinth flow, but to reduce the velocity gradient between these two flows in order to reduce losses through viscous dissipation.

For the baseline and turning device configurations, the mixing between seal carrier and labyrinth flows occurs at a radius of approximately -15% span whereas it occurs at -3.5% span for the TD-P configuration, closer to the rim seal exit. Thus, the low momentum seal carrier flow is still visible at the rim seal exit for the TD-P configuration, whereas it was fully mixed with the labyrinth flow in the other configuration. This could explained why the relative circumferential velocity was reduced with the TD-P configuration.
<figure><img src="image_7.png" /><figcaption>Figure 6: Contours of time averaged relative circumferential velocity (a) and mass- and circumferentially averaged profiles of relative circumferential velocity (b)</figcaption></figure>

As explained previously, the turning device reduces the velocity gradient between the seal carrier and labyrinth flows prior to the mixing between these two flows. The impact of this circumferential shear reduction is visible in the turbulent kinetic energy contours, depicted in the Figure 7. Regions of high turbulent kinetic energy are associated with highly unsteady flow, which therefore generates losses through viscous dissipation. The positive impact of the turning device is noticeable at the mixing area (1). By increasing the circumferential velocity of the seal carrier flow, the turning device allows the reduction of mixing losses between the two flows in the rim seal region, before exiting from the stator well cavity.

<figure><img src="image_8.png" /><figcaption>Figure 7: Contours of time averaged turbulent kinetic energy (a) and mass- and circumferentially averaged profiles of turbulent kinetic energy (b)</figcaption></figure>
The difference in turbulent kinetic energy between the configuration with turning device (TD) and with the modified platform (TD-P) may be explained by different radial velocity contours. Indeed, in the configuration with turning device, the stator vane platform induces a negative radial velocity at the deflectors exit prior to the mixing with the labyrinth flow. As depicted in Fig 8, this radial velocity is of opposite direction of the labyrinth flow radial velocity (1). On the other hand, the modified platform allows a positive radial velocity, aligned with the labyrinth flow prior to the mixing (2). This could explain the more important reduction of turbulent kinetic energy in the TD-P configuration.

<figure><img src="image_9.png" /><figcaption>Figure 8 : Contours of time averaged radial velocity for the TD case (a) and TD-P case (b)</figcaption></figure>

## Rim seal exit and second rotor inlet

Table 2 indicates the relevant quantities at the rim seal exit upstream of the second rotor row. The reduction of turbulent kinetic energy previously mentioned is clearly noticeable at the rim seal exit and indicates a reduction of viscous losses with the features. However, the relative circumferential velocity remains unchanged with the TD geometry and is even reduced with the TD-P configuration. Finally, the TD-P configuration increases the axial velocity of the fluid, which was the intent of this specific design. Thus, the difference of circumferential velocity magnitude is deteriorated in the best configuration but the direction of the fluid is closer to the main annulus one. The averaged yaw angle is equal to 65°, as detailed by Eastwood (2014).

To estimate the mixing losses of the purge flow, the momentum loss formula of Denton (1993) is used. It is given by:

$$ \xi_{mix} = \frac{2}{v_m^2} * \frac{\dot{m}_l}{\dot{m}_m} * \left[ v_{\theta_m}^2 * \left( 1 - \frac{v_{\theta_l}}{v_{\theta_m}} \right) + v_{x_m}^2 * \left( 1 - \frac{v_{x_l}}{v_{x_m}} \right) \right] \quad (3) $$

where index l and m stand for leakage and main flow respectively.

The loss coefficient for the three calculations are calculated and also presented in table 2. The highest coefficient is found for the TD-P configuration and shows that the detrimental effect of the circumferential velocity reduction outweighs the beneficial effect of the axial velocity increase.

<table><caption>Table 2 : Relevant time averaged quantities at the rim seal exit</caption><thead><tr><th></th><th>TKE (m²/s²)</th><th>W<sub>θ</sub></th><th>Alpha (°)</th><th>Beta (°)</th><th>ξ<sub>mixing</sub></th></tr></thead><tbody><tr><td>BSL</td><td>523.2</td><td>-30.52</td><td>80.452</td><td>-54.96</td><td>0.00641</td></tr><tr><td>TD</td><td>450.7</td><td>-30.48</td><td>82.036</td><td>-59.71</td><td>0.00629</td></tr><tr><td>TD-P</td><td>361.3</td><td>-41.82</td><td>78.966</td><td>-61.60</td><td>0.00673</td></tr></tbody></table>

Finally, figure 9 shows the mass- and circumferentially averaged profiles of the turbulent kinetic energy at the second rotor inlet and the rotor row efficiency difference against BSL case.
Despite less favorable circumferential velocity at the rim seal exit for TD-P configuration, the strong reduction of turbulent kinetic energy in the purge flow is recovered at the second rotor inlet. Thus, as shown with the stage efficiency difference, this reduction of turbulent kinetic energy is beneficial for the rotor and allows an increase of the efficiency stage. Thus, it seems that the turbulent kinetic energy plays a key role on the rotor performance.

<figure><img src="image_10.png" /><figcaption>Figure 9 : mass- and circumferentially averaged profiles of turbulent kinetic energy (a) at the rotor 2 inlet and rotor row efficiency difference (b)</figcaption></figure>

As a result, the overall efficiency gain with the turning device on the configuration TD and TD-P is explained by the gain found in the rotor 2. Finally, the reduction in mixing losses while the cooling flow is exhausted into the main flowpath has a beneficial effect on the downstream rotor. Even if the rim seal exit conditions seems unfavorable in the TD-P configurations, the overall efficiency is improved by the better mixing in the rim seal thanks to the turning device.

## CONCLUSIONS

In this paper, a feature to reduce the mixing and subsequent row losses has been numerically assessed in a two-stage axial turbine. The purge flow studied in this configuration consists of two leakage flows that are mixed upstream of the rim seal region, before exiting into the main flowpath. The evaluated feature is a turning device, intended to increase the circumferential velocity of the flow passing through it in order to reduce the mixing losses between the two leakage flows. A configuration with turning device associated with a modified stator vane platform to alter the radial and axial velocity of the flow was also evaluated.

Results have shown an increase in overall efficiency of 0.079% for the turning device only and 0.114% for the turning device associated with the modified platform. The increase in circumferential velocity by the turning device leads to smaller shear stress and less turbulence during the mixing of the two leakage flows in the rim seal region, by reducing the velocity gradient between them. The modified platform allows a better alignment in terms of radial and axial velocity and further reduces the turbulent kinetic energy compared to the case with turning device alone. The resulting mixing losses are then reduced in the rim seal regions, before exiting the cavity.

This effect extends to the mainflow path and its subsequent blade row with an improvement of the rotor efficiency. This improvement is linked to the reduction of turbulent kinetic energy of the purging flow and shows how the reduction of mixing losses drives the overall efficiency gain.

The turning device was added before the second stage with an impact on the overall turbine efficiency. In this configuration, about 45% of the turbine torque is produced by the second rotor row. Therefore, it may be expected that a similar fashioned turning device has a comparable additional impact if it was also added before the first rotor row.

## ACKNOWLEDGMENTS

The authors would like to acknowledge Safran Aircraft Engines specialists for their technical support and for the technical validation of this work. A special mention must be made to the MAGPI team for the geometry data that was provided, making this study achievable.

The present investigation is supported by ANRT (Association Nationale de la Recherche et de la Technologie).

## NOMENCLATURE

* k Polytropic coefficient [-]

* $\dot{m}$ Mass flow rate [kg.s⁻¹]
M Torque [N.m]

P_s // T_s Static pressure [Pa] // Static temperature [K]

r Air specific gas constant [J.kg⁻¹.K⁻¹]

V, W Velocity and relative velocity magnitude [m.s⁻¹]

V₀, W₀ Circumferential and relative circumferential velocity [m.s⁻¹]

Vx Axial velocity [m.s⁻¹]

Greek

α Flow yaw angle [°]

β Relative flow yaw angle [°]

ξ Mixing losses coefficient

ηp Polytropic efficiency

ω Rotationnal velocity [rad.s⁻¹]

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