2.1 Geometry and operational points

An HPC representative geometry of a commercial twin-spool engine was selected as the study object. Similar machines are currently in-service on large business jets, as well as regional airliners with up to 80 passengers. It is displayed in Fig. 2. Modeling efforts and modifications were focused on influencing the fore-to-last stage (stage 9) following the approach taken by Rockel et al. [Reference Rockel, Weihard, Hachmann, Hupfer and Kau8] for the rotor and by Schmidt et al. [Reference Schmidt, Gümmer and Konle14] for the casing. The main reasons for the choice are summarised below:

• • Rear compressor stages present the largest relative tip clearances, due to smaller blade heights.

• • Stage 9 is far enough from the vortex reducer and from the rear cone, which allows simplifying the model to a single blisk fixed to the surrounding structure by its lateral flaps.

• • The double-walled section of the casing is an assembly of annular flanges, less subject to heat-induced non-axisymmetric deformation effects (ovalisation), which eliminates the necessity of modeling the whole 360 ${{\rm{\;}}^ \circ }$ circumference.

• • Modeling the complete double-walled structure between the two external flanges allowed simplifying structural fixation, as well as considering the influences of bleed flows upon the casing thermal response.

Figure 2. Cut view of representative HPC chosen for the study.

Lattime and Steinetz’s review [Reference Lattime and Steinetz1] shows that axisymmetric thermal and mechanical loads are responsible for at least 70% of total clearance changes. DeCastro et al. [Reference DeCastro and Melcher15] set tolerances on clearance control related to asymmetric effects at around 15% of total clearance changes. Based thereon, modeling only axissymmetric loads and setting a minimal tolerance for clearances should suffice to adequately represent tip clearance behaviour. This also justifies the adopted simplification of a rotationally symmetric model. Only a sector of 10 ${{\rm{\;}}^ \circ }$ was modeled. The decision to remove flange screws was based on the findings of Schmidt et al. [Reference Schmidt, Gümmer and Konle16]. Namely, bleed-air ports and flange screws have a negligible contribution to clearance-relevant displacements. Naturally, removing the screws and tying the flanges to one another will have an impact on local stress distributions. Those are, however, not primarily relevant for the present analysis. Finally, it was necessary to determine the material from which the structures are built. Based on Schmidt’s discussion [Reference Schmidt13], INCONEL718 was chosen as the main alloy for the structure and NiCoCrAlY for the rotor coatings. Mechanical properties were taken from previous works [Reference Brandt, Pawlowski, Neuer and Fauchais17–Reference Thompson and Hemker20].

Regarding operational data, little is generally available in open literature. At most, operational limits are available in engine certification sheets [21]. This information, along with guidelines adopted by previous works [Reference Schmidt13, Reference Rockel, Weihard, Hachmann, Hupfer and Kau8] oriented the values assumed for the design point. On- and off-design data, detailed engine station data, as well as meanline data for the HPC, were then calculated by means of the commercial performance tool GasTurb ^®. Besides meanline properties, it was necessary to estimate the properties of relevant secondary airflows. For this purpose, the airflows were modeled as inefficient, diabatic polytropic expansions, considering the discussions of Sultanian [Reference Sultanian22]. For the transients, it was necessary to model the time evolutions of all involved variables. There is, in reality, a two-way coupling between structure and surrounding fluid flows, for which sophisticated models are required. This would be an impossible task with the available resources, so a simplified approach was adopted. Merkler et al. [Reference Merkler, Staudacher, Schölch, Schulte and Schmidt5] discuss the transient behaviour of an HPC rotor disk and provide some details on the relaxation times for temperatures at different locations. Based on that, the transients were modeled by means of logarithmic functions whose coefficients depend on the prescribed relaxation times.

2.2 Numerical model and boundary conditions

The numerical model consists of a FEM implementation in the commercial software Abaqus ^®. Given the relatively small displacements, a one-directional coupling between the energy and the stress-displacement equations was assumed. This allows sequentially solving the transient heat transfer problem and then inputting the solution into the structural simulation, rather than solving a two-way coupled problem. The main advantages are the robustness of the solutions and the reduced computational times. The same approach was used by Rockel et al. [Reference Rockel, Weihard, Hachmann, Hupfer and Kau8] and Schmidt et al. [Reference Schmidt, Gümmer and Konle16]. Computations were carried out parallelised on a Unix-based high-performance computing cluster using 8 (rotor) or 16 (casing) Intel ^®Xeon E5-2690 v3 processors with 64GB of RAM.

The domain was discretised in fully integrated, quadratic elements. In this context, ‘quadratic’ translates into extra nodes added to the midpoints of edges. For a hexahedral cell, the number of nodes goes from 8 (vertices) to 20 (8 vertices + 12 edge midpoints). Additionally, the shape functions assume a quadratic polynomial form. In essence, both geometry representation and result accuracy increase, at the expense of computational effort. Element shapes and mesh structure varied according to the expected stress levels and geometry complexity. For the rotor, tetrahedral elements were used. For the casing, a mixture of structured and swept, unstructured meshing was applied. Elements were set as hexahedral. An overview of the generated meshes is provided in Fig. 3. To ensure mathematical accuracy, a grid study was performed and its results are summarised in Table 1. The three main physical parameters were compared to assess mesh convergence: von-Mises stresses, displacements and temperatures. They were tracked at points of interest (blade tips, rotor bore) and where highest stresses were expected (blade roots, front and rear casing flanges), throughout the whole transient cycles. The most refined meshes counted 230,591 elements, 348,108 nodes for the rotor and 222,487 elements, 1,079,165 nodes for the casing. Based on a compromise between the GIS results and computational effort, meshes R3 and C3 were chosen.

Table 1. Summary of grid independence study (GIS). Percentual values were calculated as ${(\Delta \phi )_{max.}} = max\left| {1 - {\phi _{finest}}\left( t \right)/{\phi _i}\left( t \right)} \right|$ for all tracked variables

Figure 3. Reference meshes for rotor (left) and casing (right).

Contact modelling was required between the various parts of the casing structure. Surface-based interactions were chosen with different properties, based on the nature of contacts (screwed, mounted, rolling). The model was supplied with static pressure loads, surrounding flow temperatures, surface emissivities and convective heat transfer coefficients. The approach was based on the work of Horn [Reference Horn12] and Rockel et al. [Reference Rockel, Weihard, Hachmann, Hupfer and Kau8]. A comprehensive overview of the considered thermal boundary conditions is provided in Fig. 4, along with a summary of relevant correlations in Table 2. Radiation was considered by applying built-in implementations available in Abaqus ^® . Based on the findings of Keller et al. [Reference Keller, Nelson, Walton, Ghosh, Tompson and Loyalka23], $\varepsilon $ = [0.1; 0.6] is reasonable for INCONEL 718. Inside this range, the emissivity was set to 0.2 after preliminary simulations revealed marginal influence. This is in line with previous findings, which support the relatively small role of radiative (10%–15%) compared to convective heat transfer inside a compressor [Reference Rockel24]. From Tirovic et al. [Reference Tirovic and Voller25] and Jalalpour et al. [Reference Jalalpour, Kim and Reda Taha26], the range for flange contact conductances in high-performance engineering applications should be about 2000–20000 W/(m ${{\rm{\;}}^2}$ K). The conductances were set to 2000 W/(m ${{\rm{\;}}^2}$ K), after initial calculations revealed again marginal changes in overall response for higher values.

Table 2. Summary of adopted correlations for convective heat transfer over the structure

^a Source: Horn [Reference Horn12].

^b Source: VDI Heat Atlas [27].

^c Source: Alexiou et al. [Reference Alexiou, Hills, Long, Turner and Millward28].

Figure 4. Meridional view of domain with considered BCs. Static pressures were also modeled for all surfaces.

3.1 External impingement

The impingement concept was conceived based on current systems present in low-pressure turbines of typical turbofan engines. The system consists of bleeding cool air from the bypass and impinging it over the structure. A conceptual sketch of it is presented on Fig. 5. The main feature of this concept is to create a localised area of high heat transfer at the expense of little bled mass flow. Another attractive feature of external impingement is its easy integration to existing geometries without the need for major restructuring, required to isolate the various flows at different pressure levels inside the casing. In order to characterise the system, a model was created using the correlation available in Florschuetz et al. [Reference Florschuetz, Truman and Metzger29] for the Nusselt number and the corrections by Goodro et al. [Reference Goodro, Ligrani, Fox and Moon30] for higher Mach numbers. Figure 6 schematically depicts the algorithm. Given a jet diameter (D ${{\rm{\;}}_j}$ ) and thermodynamic state of the fluid inside the distribution box (p ${{\rm{\;}}_{t,pl}}$ ,T ${{\rm{\;}}_{t,pl}}$ ), all other relevant quantities can be calculated. That is, jet Reynolds and Mach numbers (Re ${{\rm{\;}}_j}$ , Ma ${{\rm{\;}}_j}$ ), jet static pressure and temperature (T ${{\rm{\;}}_{s,j}}$ , p ${{\rm{\;}}_{s,j}}$ ) and the jet mass flow ( ${\dot m_j}$ ). Pressure losses and jet velocities are a function of the discharge coefficient, defined as the ratio of isentropic to real mass flows [Reference Ben Ahmed, Weigand and Meier31], or

(1) \begin{equation}{C_d} = \frac{{{{\dot m}_j}}}{{{{\dot m}_{j,is}}}}\end{equation}

where

(2) \begin{equation}{\dot m_{j,is}} = {A_j}\frac{{{p_{t,pl}}}}{{\sqrt {R{T_{t,pl}}} }}{\left( {\frac{{{p_{ex}}}}{{{p_{t,pl}}}}} \right)^{\frac{1}{\kappa }}}\sqrt {\frac{{2\kappa }}{{\kappa - 1}}\left[ {1 - {{\left( {\frac{{{p_{s,j}}}}{{{p_{t,pl}}}}} \right)}^{\frac{{\kappa - 1}}{\kappa }}}} \right]} \end{equation}

Figure 5. Conceptual design of impingement system.

Figure 6. Impingement cooling model workflow.

For the present work, the free design variable for the impingement system is the jet diameter. The total pressure and temperature are fixed by the available air in the bypass. Figure 7 displays the calculated impingement jet properties. The system is feasible as long as the jet static pressure is above the static pressure of the medium where the flow is impinging, which proved to be the case for all investigated diameters. From the results, smaller nozzles are more favourable. Considering the heat pipe design exposed in the next section, another restriction is that the complete condensator area is cooled by the impingement system. Therefore, the diameter is set to 3mm, also to ensure a static pressure safety margin. At this diameter, ${\alpha _j}$ =321.1 W/m ${{\rm{\;}}^2}$ K, ${\dot m_j}$ =0.57 g/s, N ${{\rm{\;}}_j}$ = 130 for a ${\dot m_{j,total}}$ = 74.13 g/s of impingement air. Considering the estimated mass flow of 70.46 kg/s for the bypass, the amount of required bleed air lies at 0.11% and is negligible in terms of lost fan thrust.

Figure 7. Impingement jet properties for fixed feedflow conditions (cruise-flight). Parameter range for which the model is valid: Re $ \in $ [10000,60000]; Ma $ \in $ [0.2,0.6].

In the FEM model, the impingement cooling is implemented as a surface boundary condition with the given temperature and heat transfer coefficient. The number of jets, as well as the surface area impacted, are determined considering that the pitchwise distribution of jets and the axial averaging length of Nu ${{\rm{\;}}_j}$ is equal to 5 $ \times $ D ${{\rm{\;}}_j}$ .

3.2 Concentric annular heat pipes

Concentric annular heat pipes provide improved anti-gravity operation when compared to conventional designs. This is due to the extra wick area made possible by the presence of the inner pipe wall. The design considered in this work is inspired by Zhao et al. [Reference Zhao, Ji, Yuan, Guo and Zhou32], who also proposed a composite wick design to increase the capillary limit even further for a high-temperature concentric annular heat pipe. The conceptual design of the heat pipes applied in this work is depicted in Fig. 8, along with its main dimensions, listed in Table 3.

Figure 8. Conceptual design of the concentric annular heat pipe.

From Noda et al. [Reference Noda, Yoshioka and Hamatake33], a model for the screen wick properties was derived. The results were modified to include the improvements achieved by Zhao et al. [Reference Zhao, Ji, Yuan, Guo and Zhou32]. Using the modelling approach described by Chi [Reference Chi34] and Faghri [Reference Faghri35], and applied by Nemec et al. [Reference Nemec, Čaja and Malcho36], the operational limits of the heat pipe design were calculated. The geometric dimensions of the heat pipe were set within the limits of structural accommodation on the reference casing geometry. Material properties for the working fluid were taken from Faghri et al. [Reference Faghri and Zhang37, Reference Faghri, Zhang and Howell38]. With all the parameters defined, it was possible to calculate the operational envelope of the heat pipe. It is displayed in Fig. 9 for the case in which the heat pipe is operating against gravity (i.e. the most unfavourable condition). The internal stresses were also estimated using a simple pressurised pipe model, as defined by Faghri [Reference Chi34]. Given the proposal of manufacturing the heat pipes with the same material as the casing, the estimated values are well below any material limits and were not taken as cause for concern.

Table 3. Estimated parameters of the star-forming regions in the NGC 7,252 interacting system

Working fluid: Dowtherm ^®.

Wick: 400–200 screen [Reference Zhao, Ji, Yuan, Guo and Zhou32].

Figure 9. Heat pipe calculated operational envelope for anti-gravity operation.

The heat pipes are implemented in the FEM model as individual parts composed of two different materials. The container volume is modeled as INCONEL718, with exactly the same thermomechanical properties as the casing structure. The inner volume of the heat pipe is modeled following the approach adopted by Eisemann et al. [Reference Eisenmann, Mair and Hupfer39]. That is, to consider the inner heat pipe material as having a small elasticity modulus (taken as E = 10 MPa), a very high thermal conductivity (k = 20000W/m.K), a density and specific heat which, corresponding to the mass average of working liquid and vapor, both temperature-dependent. The thermal expansion coefficient is taken as the same as for the container. That way, the high heat flow can be simulated and non-physical effects caused by thermal expansion and mechanical stress transmission are avoided. The overall heat pipe conductivity is then mainly a function of the container thickness and the wall area over which heat is transferred, which is automatically handled by the FEM solver. For the considered model, the estimated mass of one heat pipe lies at 4.7g. If they are placed circumferentially at a 5 ${{\rm{\;}}^ \circ }$ pitch (72 units), the total added weight is 338.4g. In comparison, copper bars with the same volume would weigh in total 1.86kg, roughly 5.5 times more.

4.1 Square cycle analysis

Although the lack of experimental data makes proper validation an impossible task, a qualitative comparison with selected literature sources was performed. For the rotor, temperature and stress evolutions for a squarecycle (IDLE-MTO-IDLE) are presented in Fig. 10. The data used by Merkler et al. [Reference Merkler, Staudacher, Schölch, Schulte and Schmidt5] were used as a reference for the comparison. Given that different geometries are considered and that the reference data is not plotted in absolute terms, only trends can be compared. In general, the results are satisfactory. The stress evolutions show correct trends, with compression on the rim (red curve, lower graph in Fig. 10) during the acceleration phase, followed by stabilisation at an adequate difference between stresses in different rotor heights. The opposite behaviour is seen upon deceleration. Relatively high-bore stresses are observed, which is attributed to the fact that the rotor is simplified as a blisk. The extra mass filling the actual dovetail rails add up to the centrifugal forces being transmitted to the bore. Regarding temperature distributions, the curves are closer together than for the reference, which is due to the fact that the bleed air comes not from the compressor inlet as for the reference, but from stage 6 and is thus hotter.

Figure 10. Temperature and stress evolutions for the rotor disk for a square test cycle (left). Reference measuring nodes (right). The time span was adjusted to match the curves displayed by Merkler et al. [Reference Merkler, Staudacher, Schölch, Schulte and Schmidt5].

Figure 11. Calculated tip clearances in stage 9. The time span was adjusted to match the curves displayed by Schulte et al. [Reference Schulte, Schmidt, Weckend and Staudacher6].

For the casing structure, even qualitative comparisons in terms of temperature and stress evolutions are impractical, due to the particularities of different flange designs. Therefore, the casing response was tuned based on the resulting tip clearances. Figure 11 exhibits the calculated clearance evolution for a similar square cycle. The results of the selected literature source [Reference Schulte, Schmidt, Weckend and Staudacher6] are not reproduced here, the reader is invited to make the comparison. Referring to the deceleration from MTO to IDLE (2000s–4000s), the fast opening caused by the reduced centrifugal forces is followed by a closing caused by the cooling casing. The rotor blisk, more massive, takes longer to cool. Its cooling leads to the final clearance opening towards the stationary level.

4.2 Influence of implemented TCC concepts

For evaluating the concepts, the test cycle consists of an acceleration to MTO until a stationary regime is reached, followed by a deceleration to steady ADP conditions. The whole cycle consists of 4000s, 1500s for the MTO phase and 2500s for the ADP one. The impingement system is turned on 300s after the start of the ADP phase. Figure 12 exhibits the FEM implementation of the concepts. Notice the position of the proposed heat pipe fixation in the structure, between stator 9 and rotor 10. In Fig. 13, some effects can be observed on the transient clearance curves of the different concepts. Firstly, the heat pipe decelerates the casing response to the new operational point conditions. That is reflected by a lower clearance peak after the initial pinch point at the beginning of the MTO phase ( $\sim$ 100s). Regarding ADP clearances, isolated concepts had no effect whatsoever. For the external impingement, this was expected, given the local cooling action. For the heat pipes, some appreciable effects were expected, however not seen. As it will become clear further in this work, the condensator cooling magnitude, the position and quantity of heat pipes have a defining effect over their influence. In fact, the combined concept implementation already hints at it. A very small clearance reduction was achieved for the rotor (1.69%–1.59% or 0.1%). For the stator, the effects are more pronounced (1.60%–1.31% or 0.29%). Still, a relatively small influence.

Figure 12. 10 ${{\rm{\;}}^ \circ }$ pitch HP concept. In red, impingement BC surface.

Figure 13. Clearance evolutions for implemented concepts.

Figure 15 displays the von-Mises stresses for the critical region of the casing at cruise. The tendency to ‘bend’ forward due to the higher temperatures at the rear part generates the highest stresses at the front flange. For the reference, they reach 861 MPa for the MTO phase and level out at 632 MPa for cruise conditions. While the heat pipe along does not have appreciable effects over the critical stresses, the external impingement scheme actually reduces them to 494 MPa. This is due to the overall temperature reduction at the rear casing section. Naturally, there is a redistribution of stresses, not shown here, to other flanges at the rear part. However, the absolute stress values remain lower than the critical one. There is only one exception to this, at the bore introduced on the outer casing structure to accommodate the heat pipe. The expected geometry-induced stress concentration is enhanced by the large temperature difference caused by the impingement system, which leads to stresses up to 892 MPa at cruise. The corresponding contours are displayed in Fig. 14. A possible solution for this issue could be achieved by thermally isolating the casing structure under the impingement jets, so that the cooling effect is restricted to the HP condensators. It is to expect that any modifications on the original structure will also impact its dynamic response, mostly concerning the shifts in mass distribution created by adding the heat pipes. Aeroelastic analyses, especially concerning fluid-structure interactions, are quite sensitive to the local, unsteady flow conditions. Such level of detail is out of the scope of this preliminary investigation, and the required data is not available.

Figure 14. Stress concentration at heat pipe bores.

Figure 15. Temperatures at rear part of casing (left) and Von-Mises stresses in critical region (right) for the implemented concepts.

One last aspect worth mentioning relates to Fig. 9, the operational envolope of the heat pipe. At ADP, the heat pipe’s temperature remains almost constant at 502 K. During the MTO phase, without cooling, it rises to 744 K. For the first condition, the maximum heat flux inside the heat pipe reaches 43.9 W/cm ${{\rm{\;}}^2}$ . For the last, it stays at 7.4 W/cm ${{\rm{\;}}^2}$ . Considering the calculated operational envelope, dry-out should occur for the MTO condition, while safe operation seems feasible for the ADP phase. Whether exposition to such high temperatures is an issue or not requires further investigation. Two main aspects here are the recuperation of dry-out and working fluid decomposition. Considering dry-out, Baraya et al. recently showed the possibility of normal operation restablishment, with some temperature hysteresis [Reference Baraya, Weibel and Garimella40]. For the intended operational point, the heat pipes can still be pushed considerably to lower temperatures to allow increased heat flux.

4.3 Influence of HP distribution

Considering the local influence of the heat pipes and the direct dependency between flange temperature and displacement (i.e. clearance), the influence of increasing the quantity of heat pipes (reducing the pitch), as well as the effects of changing their attachment position to the structure were investigated. For clarity, the FEM implementation for the 5 ${{\rm{\;}}^ \circ }$ at the frontal position is displayed in Fig. 16. They are fixated between both vanes of stage 9, so as to have local action over the coatings of rotor 9.

Figure 16. 5 ${{\rm{\;}}^ \circ }$ pitch HP concept. In red, impingement BC surface.

The obtained clearance curves are summarised in Fig. 17. The effect of positioning the heat pipes closer to the rotor is evident by comparing the respective curves (green and cyan). Rotor 9 clearances go from 1.69% to 1.50% to 1.24% considering the reference, 5 ${{\rm{\;}}^ \circ }$ pitchwise rear and front positionings, respectively. This means a reduction in 0.29% and 0.45% clearance for the same impingement cooling. There is some penalty in the stator 9 clearances, from 1.09% to 1.17% (or 0.08% increase) when moving the heat pipes axially towards the rotor. In essence, the benefits outweigh the costs. Additionally, these results further confirm the local action of the cooling system. Regarding the quantity of heat pipes, the results are quite intuitive. The more heat pipes, the more heat transfer, the lower the temperatures and, therefore, the tighter the clearances.

Figure 17. Clearance evolutions for different pitchwise and axial distribution of heat pipes.

Figure 18. Stress concentration at heat pipe bores for configuration of Fig. 16.

Regarding stresses, the modified configuration exhibits a similar behaviour to that discussed in the previous section. The peak stresses at the casing front flange increase by little, going to about 878 MPa. The heat pipe bore holes added to cooling cause a stress concentration. However here, an additional benefit of the different heat pipe positionining becomes evident. The generally lower stress level at the front position lead to lower concentrated stress at the bores, as displayed in Fig. 18, with peak of 601 MPa on the bores for the ADP phase.

The last aspect relates to safe heat pipe operation. The discussion is similar as before, for the 10 ${{\rm{\;}}^ \circ }$ pitch case. The operational temperatures go up to 788 K during the MTO phase, with a reduced heat flux of only 3.5 W/cm ${{\rm{\;}}^2}$ . During the ADP regime, HP temperature stabilises at 471 K with a heat flux of 37.7 W/cm ${{\rm{\;}}^2}$ . Also for this configuration, the improvement potential through enhanced condensator cooling is evident. Dry-out and working fluid decomposition during critical operation might pose an obstacle to an actual implementation.

4.4 Influence of cooling magnitude

Building on the previous discussion on the available operational envelope for cruise conditions, the impingement cooling was artificially enhanced to assess its influence over the system’s response in terms of clearance. Figure 19 depicts the steady clearances at cruise for different impingement heat transfer coefficients. There is a slight tendency towards saturation, expected as the temperature of the heat pipes approaches that of the cooling air. The right side of Fig. 19 clarifies the tendency towards saturation. The theoretical limitation is to have a large enough cooling to equalise heat pipe and impinging air temperatures. Considering T ${{\rm{\;}}_j}$ = 279.2 K, the required magnitude of ${\alpha _j}$ would make it impractical to reach this lower limit, and already at the tested levels, the benefits become marginal when compared to the corresponding cooling enhancement. This is naturally a very simplified first assessment. Relatively simple cooling enhancement techniques, such as adding fins to the heat pipe condenser, might be worth more attention.

Figure 19. Variation of ADP clearances, HP temperature and max. heat flux with ${{\rm{\alpha }}_{\rm{j}}}$ .

4.5 Clearances under slam acceleration

As a final round of assessment, the system’s behaviour was analysed under a strong transient, which could potentially bring the rotor blades into rubbing danger. The test slam cycle comprises a stabilisation in cruise conditions (ADP) followed by a deceleration to high-altitude idle (HIDLE) for 100s and a consecutive acceleration to the top-of-climb condition (TCL) over another 100s, then followed by a restabilisation in ADP. Provided the impingement system is on only during the cruise phase, this transient slam cycle reflects a situation where the aircraft is required to descend for a short period and then suddenly ascend again, for example as a dodging manoeuver to avoid incoming air traffic. Other common critical transients, such as an aborted landing, are not addressed, because the system would not be active during this flight phase. Only the combined concept with 5 ${{\rm{\;}}^ \circ }$ HP pitch and frontal positioning was simulated (see Fig. 16). Two control cases were investigated for the impingement system. The first one was to simply leave it on during the whole transient manoeuver. The second involved turning off the system at the start of the deceleration and turn it on after 100s of stable cruise regime. The respective results are shown in Fig. 20.

Figure 20. Clearance evolutions for high-altitude slam transient cycle.

The system’s influence over the transient is noticeable for the continously on case. Pinch clearances reach a value as low as 0.63%. For the reference, the minimum clearance is 0.98%, quite close to the steady MTO one. Turning the system off improves the critical clearance in 0.24%, with a minimum of 0.87%. The stator shows a similar trend, with 0.90% for the reference compared to 0.54% for the continuous impingement case and 0.74% for the off-on case. Although conclusions on rubbing cannot be drawn at this point, the model shows that a robust control system can mitigate transient rubbing dangers by controlling the amount of impinged air and potentially its temperature.

5.1 Outlook

This paper is part of a larger project aimed at assessing the potential and laying the foundations for thermal TCC in future compressor systems. Interest in such technologies anticipates issues inherent to designs with higher overall pressure ratios, i.e. larger relative clearances. Follow-up work being carried out involves detailed, reliable modeling of heat pipes to enable proper structural integration and design optimisation, in addition to closer insight on limiting phenonema such as the wick’s capillary limit. The dynamic perspective must also be considered, especially concerning local shifts in mass distribution on the casing. Further ahead, a detailed model for the impingement cooling is planned, also aimed at system optimisation and control. Rig testing at representative conditions is also a requirement to properly validate numerical results. If established, actively cooled heat pipes might find a whole new high-performance application field within aeroengine compressors.