GT HEAT TRANSFER IN TURBINE HUB CAVITIES ADJACENT TO THE MAIN GAS PATH

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1 Hot gas ingestion Cooling air Cooling air Proceedings of ASME TURBO EXPO 2010 Power for Land, Sea and Air June 14 18, 2010, Glasgow, UK GT HEAT TRANSFER IN TURBINE HUB CAVITIES ADJACENT TO THE MAIN GAS PATH Jeffrey A. Dixon, Antonio Guijarro, Andreas Bauknecht Rolls-Royce plc, Derby, UK Daniel Coren, Nick Atkins TFMRC, University of Sussex, Brighton, UK ABSTRACT Reliable means of predicting heat transfer in cavities adjacent to the main gas path are increasingly being sought by engineers involved in the design of gas turbines. In this paper an interim summary of the results of a four-year research programme sponsored by the EU and several leading gas turbine manufactures and universities will be presented. Extensive use is made of CFD and FE modelling techniques to understand the thermo-mechanical behaviour of a turbine stator well cavity, including the interaction of cooling air supply with the main annulus gas (see Figure 1). The objective of the study has been to provide a means of optimising the design of such cavities for maintaining a safe environment for critical parts, such as disc rims and blade fixings, whilst maximising the turbine efficiency, and minimising the fuel burn and emissions penalties associated with the secondary airflow system. The modelling methods employed have been validated against data gathered from a dedicated two-stage turbine rig, running at engine representative conditions. Extensive measurements are available for a range of flow conditions and alternative cooling arrangements. The analysis method has been used to inform a design change which is also to be tested. Comparisons are provided between the predictions and measurements of the turbine stator well component temperature. INTRODUCTION The requirement for ever more efficient gas turbine engines is leading to increased gas path temperatures, creating increasingly hostile environmental conditions for the adjacent turbomachinery and support structures. Cooling air systems are designed to protect vulnerable components from the hot gas that would otherwise be entrained into the cavities communicating with the gas path through the inevitable gaps between rotating and static parts. These cooling flows are bled from the compressor stages and reduce the engine efficiency, as they can represent around 20% of the total main gas path flow. These performance penalties manifest themselves in two ways, i.e. having a direct impact on thermodynamic cycle performance, resulting from imperfect work extraction in the turbines, and in the spoiling effect of the efflux at the point where it re-enters the turbine main annulus flow, causing a reduction in stage efficiency. It is desirable therefore to minimise these cooling flows, to levels consistent with maintaining the optimum component lives and the mechanical integrity of the engine. Cooling air Hot gas ingestion Cooling air Figure 1 Typical turbine stator well Under the auspices of the European Commission Programme for Research and Technological Development Framework 6 - Aeronautics and Space, a consortium of European gas turbine manufacturers and universities has undertaken a four-year project to address this specific issue. This project is called Main Annulus Gas Path Interactions or MAGPI [1]. There are 5 work-packages in this project and the first of these is specifically aimed at turbine disc rim cavity heat transfer and cooling optimisation. This work builds on a previous study [2], both extending the methodology, and improving the quality of the test data used to validate the method. This paper presents a description of the up-dated rig test facility and the numerical analysis work performed by some of the partners in the consortium. The aim of the work has been to further advance the understanding of cooling flow, annulus gas interaction and resultant heat transfer, in the cavities adjacent to the main annulus in multi-stage turbines, in particular: 1 Copyright Rolls-Royce plc 2010

2 The flow distribution and mixing which take place in the turbine stator well. The influence of the geometrical features such as cooling air entry holes and interstage seal clearance. The interaction between the disc rim boundary layer and the main annulus gas ingestion flows. Finite element and computational fluid dynamics models have been created to further improve the analysis tool-set and best practices for turbine stator well design. A coupled analysis technique [3] has been further developed, which enables the direct application of convective heat fluxes generated in the cavity CFD solutions, to be applied to the finite element models representing the engine hardware. This modelling capability is being validated using measured data from the two-stage turbine facility sited at the University of Sussex. Both steady and unsteady CFD solutions are presented, with comparisons to measured data. Alternative cooling configurations have been both modelled and tested for a range of cooling flow levels. Additional work has been done to predict the potential benefits of further design changes, which will also be tested in the rig as part of the MAGPI programme. NOMENCLATURE C p Specific heat capacity at constant pressure [J/kg.K] C v Specific heat capacity at constant volume [J/kg.K] C Constant used in definition of turbulent effective viscosity, = 0.09 [-] g Acceleration due to gravity [m/s 2 ] h Surface heat transfer coefficient [W/m 2.K] I Turbulence intensity [-] k Thermal conductivity [W/m.K] k Turbulent kinetic energy [m 2 /s 2 ] k P Turbulent kinetic energy at near-wall point P [m 2 /s 2 ] y Normal distance from the wall [m] R Gas constant [J/kg.K] T Fluid temperature [K] Non-dimensional temperature [-] p Fluid static pressure [Pa] p t Fluid total pressure [Pa] p Non-dimensional pressure [-] u y P Friction velocity = ( W/ ) 1/2 [m/s] Near-wall distance to point P [m] Thermal expansion coefficient [K -1 ] T Surface to fluid temperature difference [K] Dissipation rate of turbulent kinetic energy [m 2 /s 3 ] Fluid thermometric conductivity = k/(.c p) [m 2 /s] Fluid dynamic viscosity [kg/m.s] Fluid kinematic viscosity, / [m 2 /s] Fluid density [kg/m 3 ] Angular velocity [rad/s] C/A Cooling air (as in C/A mass flow) [kg/s] Gr Grashof number, g.. T.L 3 / 2 [-] Nu Nusselt number, h.l/k [-] Pr Prandtl number, C p. /k [-] Re y Near wall Reynolds number,. k.y/ [-] u + Shear stress near wall velocity / )( u/ y) y=0 y * Non-dimensional wall distance,.c 1/4.k 1/2 P.y P/ [-] y + Non-dimensional wall distance,.u.y P/ [-] THE TEST FACILITY All tests were carried out at the University of Sussex, Thermo-Fluid Mechanics Research Centre. The test facility is shown in Figure 2. A brief overview is given here, full details can be found in Coren et al. [13] Drive arm Stator 1 Exhaust Figure 2 Turbine Rig Test Facility The test section of the rig comprises a two-stage turbine, rated at 400kW, with a pressure ratio of approximately 2.5 at the design condition. Flow coefficients are 0.51 for stage 1 and 0.62 for stage 2, with work coefficients of 1.6 and 1.4 respectively. Main annulus air is supplied to the rig by an adapted aero engine driven compressor plant at 4.9 kgs -1, 3.3 bar absolute and approximately 170 C. An Atlas Copco screw type compressor is used to provide the various cooling air supplies. The cross section of the rig test section (Figure 3) has been designed to represent the key features of a turbine stator well. The turbine has also been designed to suit the subsequent FE and CFD analyses, with 39 nozzle guide vanes and 78 rotor blades for each stage. Thus the analysis models can be set-up at 1/39 th of the complete rotor/stator system. Cooling Geometry and Supply The cooling air is supplied to the hub region of the test rig via insulated transfer tubes. The rig has a split casing and is designed to allow rapid geometry changes. Figure 3 Turbine rig section Inlet Dynamometer Downstream cavity 2 Copyright 2010 by Rolls-Royce plc

3 The coolant may be introduced to the upstream stator well either radially through removable threaded inserts, or axially through removable cover plates with slot exits representing lock plate and blade fixing leakage paths. This arrangement allows 0, 13, 26 or 39 flow exits to be used at each entry point. These features are highlighted above in Figure 3. The signals from the thermocouples installed on the rotating assembly are transmitted using a 92 channel radio telemetry unit, with custom cold junction referencing, located upstream of the test section. Figures 5 and 6 provide an overview of the test section temperature and pressure instrumentation respectively. Figure 4 Cooling Flow Paths In order to achieve accurate metering of coolant to the stator wells, the delivery path is separated from the outer wheel space by a balance cavity sealed by two labyrinth seals. During testing this cavity is pressure balanced against the higher pressure coolant supply to prevent leakage; effectively forming a blown seal. The balance air is measured upstream of the rig, and vented from the intermediate wheelspace to prevent egress into the main annulus. This arrangement also allows a known rate of egress to be specified. Cooling air flow rates are determined using hot film air mass meters. Instrumentation Turbine main annulus conditions are measured by temperature and pressure probes built in to the leading edges of the NGVs, avoiding the blade passage restrictions inherent with inter-stage probes. The turbine stator well and surrounding regions have been instrumented with metal and air thermocouples and static pressure tappings. Figure 6 Pressure Measurement Positions NUMERICAL MODELING The overall objective of this study is to improve the modelling capability for turbine stator wells, i.e. cooling flow distribution and heat transfer management, with a view to optimising disc rim cooling and component life. It is anticipated that this will lead to further development of coupled FE/CFD modelling techniques [3, 4 and 5]. Finite Element Thermo-mechanical Models In preparation for this objective FE models of the rig (2D axisymmetric) and test section (3D), have been created. Appropriate solid properties, e.g. thermal conductivity as a function of the metal temperature, are modelled. The 2D model being first used in the rig design phase to help establish operating temperatures, stress levels and clearances etc. See Figure 7. Figure 5 Temperature Instrumentation Figure 7 Finite Element model This model has been used to reproduce the measured temperatures indicated by the thermocouple positions from the test facility. The CFD solution can be used to replace the more usual, empirical correlation based, boundary 3 Copyright 2010 by Rolls-Royce plc

4 conditions on the FE model, i.e. to establish the disc rim cavity convective heat transfer (heat fluxes). Together they form the coupled FE/CFD solution, which can then be validated against measured surface temperatures from the test rig. An in-house computer code [7] has been used to generate the finite element thermo-mechanical models. The coupling of this code to the commercial CFD analysis program Fluent [8] was reported in [2]. This methodology, first developed by Verdicchio [6], subsequently enhanced in collaboration with the Universities of Sussex and Surrey [3,4,5], is now the chief means of validating the CFD method for convective heat transfer in the stator well. A further development allows us to use an in-house CFD code Hydra [9] for the determination of cooling flow distribution and convective heat transfer, in place of the commercial code. Computational Fluid Dynamics Models In parallel with the development of the test facility, it has been necessary to further develop the CFD modelling capability required to analyze the flow and heat transfer in the turbine stator well. It has now been shown that this requires both steady and unsteady calculations in full 3D, particularly where cooling efflux and annulus gas ingestion are finely balanced. However in other flow conditions, e.g. un-cooled stator wells a steady solution is adequate. The suitability of a sector model chosen to keep the computational requirements within the capability of available computer facilities is still not certain, but initial results are encouraging. The test facility was developed with this limitation in mind and the current CFD model is 1/39 of the full rotor/stator system, i.e. incorporating 1 NGV, two rotor blades, one cooling air hole or one lock-plate slot, see Figure 8. Figure 9 Interstage rim gap mesh. Interface planes Figure 10 CFD Mesh Interface Planes At this stage the in-house CFD analysis code Hydra [9] is used. Note: Other partners in the consortium are using different commercial CFD codes [10]. Flow and pressure input boundary conditions were as measured on the test facility. Figure 8 CFD analysis model The computational domain was meshed using the inhouse software PADRAM (Parametric Design and RApid Meshing). This automatic meshing tool produces high fidelity fully structured meshes. Around a million cells per vane plus four million cells in the stator well cavity grids were created. A detail of the rotor 1-stator 2 rim gap mesh is shown in Figure 9. The domain was split in three zones separated by mixing or sliding planes where required, (i.e. steady state or unsteady calculations). The first zone contained the first NGV, the second both rotors linked by the cavity radially inboard, and the third region contains the second NGV in between both blades. Each vane was meshed separately. In addition, the rotor vanes included half the cavity in each of the rotor domains. The resulting three zones were merged into a single domain. Figure 10 shows the interface planes. Turbulence Modelling The Spalart-Almaras turbulence model has been chosen for these calculations. Rolls-Royce plc has extensive successful experience of using Spalart-Almaras for main gas path flows, as well as for fluid flow and heat transfer in secondary flow cavities, using the in-house code. This has allowed benchmarking of the turbulence models used by the MAGPI partners. The CFD mesh has been adjusted to ensure that the majority of the y + values are within the recommended range for the Spalart-Almaras turbulence model, (between 20 and 40), with the standard wall treatment of Spalding [11]. In the small gaps, such as the labyrinth seal and rotor/stator rim, there are difficulties in maintaining this constraint, and in some places the y+ values are within the viscous sub-layer region. In that case Hydra mimics the low Re Spalart- Almaras model [12], by ensuring u+=y+. Such functionality (i.e. Hydra reverting back to viscous sub layer), is useful in handling the trailing edge flow, where the scale of the 4 Copyright 2010 by Rolls-Royce plc

5 circulation after the separation (Figure 11), requires high mesh resolution that can only be met by having y+<5. Wall total temperatures, torque and power monitors were set to ensure convergence in the models. It has been noticed, however, that to achieve full convergence in Hydra with this turbulence model, a larger number of iterations is required. The Spalart-Almaras model was originally created to better capture the separation in the boundary layer, selecting this to get more accurate predictions of the heat transfer in the rotor walls. However, this model, having just one additional turbulence equation, has been observed to struggle to drive the heat to the core of the recirculation vortexes, such as in the middle of the downstream cavity. Hence, instead of being able to achieve a converged solution within a couple of thousand iterations, typical for main annulus compressor or turbine calculations, this model, including the stator well, required about 20,000 iterations. to accurately model turbine stator fluid flow and heat transfer. From the first phase of the test programme an extensive range of good quality data is now available for the datum rig geometries, i.e. drive arm cooling holes and lock-plate slots. Main annulus pressures Figure 11 Rotor 1 trailing edge model The disc surface thermocouple measurements facilitate validation of the method for this application, now that the fully coupled FE/CFD analysis capability has been established. OBJECTIVES The objectives of the modelling capability are to enable the optimum level and placement of cooling air for disc rim environmental control (cooling). This includes the determination of cooling flow re-ingestion, i.e. from the upstream efflux at the front of the stage 1 disc rim, some of which is drawn into the turbine stator well cavity. The most efficient use of the cooling air is to be achieved by judicious placement of this air and the optimisation of the stator well geometry. Each of these aspects is being investigated by partners in the MAGPI Work-package 1 consortium, with data being generated on the test rig at the University of Sussex, to validate the methods used. Some of this work is still to be completed and will be published at a later date. However some results are available now and these will be presented in this overview paper. RESULTS CFD Analysis Main Annulus The primary aim of the rig test programme was to generate a good range of high quality test data that can be used to assess the capability of the coupled FE/CFD method, Main annulus temperatures Figure 12 Data Comparison Positions Comparisons have been made with main annulus pressure, temperature and mass-flow measurements. Figure 12 shows the pressure tap and thermocouple rake locations used to compare measured and predicted pressures and temperatures in the main gas path. Figure 13 shows the CFD model predictions for total temperature at four plane sections (corresponding to the rake locations in Figure 12). Details, such us the trailing edge wakes or the secondary flows are captured, as can be seen when looking at the higher radial plane, (Figure 13). r=0.158 m r=0.162 m Figure 13a CFD Model Validation Main Annulus 5 Copyright 2010 by Rolls-Royce plc

6 compressor Venturi tube. However, the measured temperature at the NGV 1 rake is around 1% lower, probably due to heat losses in the inlet system. The pressure predictions are also close to the measurements, the maximum difference is less than a 3% in the worst case. r=0.168 m r=0.173 m Figure 13b CFD Model Validation Main Annulus The model was run to a number of coolant mass flow rates, fed into the stator wall cavity by means of the drive arm hole. The mass flow rates are detailed in Table 1 as a percentage of the main stream flow. Two representative cases are presented here, i.e. coolant flows of 0.61% and 1.12%. Table 1 provides more detailed information on the differences between the total pressures and absolute temperatures predicted, with the available measured data. The values have been made non-dimensional dividing by the measured or area averaged inlet total temperatures and pressures (respectively for experimental data or analysis results). The CFD analysis has chiefly been conducted for the rig design point, with updated inlet temperature boundary conditions, to allow better benchmarking with the test data. Additionally, this design point analysis has allowed a comparison of solutions for different cooling air rates delivered through the drive-arm hole locations. Alternative meshing approaches The possibility of using a hybrid mesh for the stator well cavity has been investigated. The structured grid of the main annulus remains unchanged whereas a circumferentially swept 2D unstructured grid with a prismatic o-grid layer is used for the stator well cavity. This alternative approach reduces meshing time significantly and additionally, allows the handling of complex geometries in a convenient way. These capabilities are required for future implementations (geometry optimisation) that will be subject of the Test Phase 2 analysis. (a) Structured mesh % (b) Unstructured Coarsest mesh within this study (0.7 million nodes) Table 1 Measurements Vs Prediction Good agreement has been achieved between the experiments and the simulations. The higher discrepancies were found at the thermocouples in the secondary flows. Nevertheless, one of the most important sources of error seems to be the difference between the inlet boundary condition and the actual inlet temperature. The data has been read from the measured temperature in the DART (c) Unstructured Finest mesh within this study (4.2 million nodes) Figure 14 Examples of the meshing approach 6 Copyright 2010 by Rolls-Royce plc

7 Mach Number [-] Absolute Total Temperature [K] Absolute Total Temperature [K] A mesh sensitivity study has been carried out, varying the number of nodes of the cavity mesh. This has been done using the in-house software PADRAM (Parametric Design Rapid Meshing), in its un-structured version, which is developed and maintained by the Aerothermal Methods Group at Rolls-Royce plc. In brief, the mesher generates a 2D mesh based on Delaunay triangulation with an O-grid determined by the user. The cavity mesh matches the existing main annulus grid, which is swept in the tangential direction. Using this application the mesh of the stator well cavity is generated within seconds. The study was carried out comparing the results with those obtained with the structured grid. Figure 14 shows examples of the meshes created during the study. Name Nodes Prism. Layer y+_min y+_max M M No refinement M M Light M refinement M M Strong refinement M M Optimisation St 4.2 M Baseline _0.9M 17_1.1M 22_4.0M 23_1.8M St_4.1M Axial coordinate [mm] Figure 15 shows the absolute total temperature in the cavity at radius r = m. This comparison indicates that both the coarse (16 and 17) and the fine grids (22 and 23) provide a fairly accurate CFD prediction. Nevertheless, the finer meshes match the structured grid more accurately. Despite this, the differences in temperature in this plane are below the margin considered as acceptable for the grid validation _0.9M 17_1.1M 22_4.0M 23_1.8M St_4.1M Table 2 - Overview of unstructured meshes The possibility of using a coarse mesh to speed up the CFD run-time, while providing a fairly accurate CFD prediction at the same time, has been investigated. The number of nodes has been varied by changing the size of the cells in the inner mesh and also by modifying the characteristic of the prismatic layer. This number varies from 0.7 to 4.2 million nodes. All cases have been run in Hydra [9] and post-processed to the MAGPI WP1 design point condition. Note: All with no ingested coolant, and adiabatic walls. They have been compared to each other, and to the solution given from the previous model using a structured mesh. A selection of coarse and fine grids has been made in order to do further investigations. In total, 10 meshes were created with different levels of refinement and prismatic layer width and nodes in order to keep a smooth transition between the tetrahedrons and the prisms. From these, four were selected as the most representative cases: two coarse grids with under a million nodes, and a fine prismatic layer within the normal y+ values, a very fine mesh comparable to the structured grid with y+ values of the order of unity, and an intermediate grid with similar near wall distance to the hexahedral mesh. Table 2 provides details of all the relevant meshes created, including the number of nodes and the minimum and maximum y+ values Axial coordinate [mm] Figure 15 - Absolute Total Temperature r=0.115 m This effect can be seen in Figure 16, where the Mach Number for the same radial cut is shown, and in Figure 17 which shows the total pressure in the downstream cavity at the axial position x = m. Again the finest mesh provides the closest solution to the structured mesh _0.9M 17_1.1M 22_4.0M 23_1.8M St_4.1M Axial coordinate [mm] Figure 16 - Mach number at r = m 7 Copyright 2010 by Rolls-Royce plc

8 Radial position [mm] 16_0.9M 17_1.1M 22_4.0M 23_1.8M St_4.1M Total Pressure [kpa] Figure 17 - Total Pressure at an axial plane These results imply that a good agreement can be achieved using only the half the number of nodes, which also means a much lower CPU run-time. This suggests that, during the analysis task for Test Phase 2, representative predictions could be achieved using a rather coarser mesh for the stator well cavity. If a very accurate solution is required the transition to a fairly fine mesh should be made. The CFD mesh has been adjusted to ensure that the majority of the y+ values are within the recommended range for the Spalart-Almaras turbulence model with standard wall treatment. Cavity results: Adiabatic and non-adiabatic walls From the first phase of the test programme an extensive range of good quality data is now available for the datum rig geometries, i.e. drive arm cooling holes and lockplate slots. From all the experiments carried out, the data from the tests shown in Table 3 has been extracted and used to compare the fluid total temperatures predicted by the CFD solution. In addition, the relative importance of the application of wall temperature boundary conditions and the viscous heating against the heat conduction in the fluid, has been analysed. Table 3 shows the comparison of absolute total air temperature in the cavity (in non-dimensional form, ), i.e. test data, with the CFD predictions. The last two columns represent the difference in temperature as predicted, minus the measured value. Two cases have been run considering an adiabatic solution (A) and a non-adiabatic solution (NA). At each wall inside the stator well cavity, temperature profiles have been applied. These temperature distributions have been generated interpolating linearly between the measured temperatures at the metal thermocouple locations. Hence, two cases have been generated for each cooling flow distribution, namely the adiabatic and the non-adiabatic solution. The comparison shows good agreement for the CFD predictions, where temperature profiles had been applied. Figure 18 Air thermocouple locations Figure 18 shows the air thermocouple locations in the cavity. As expected, the application of temperature profiles at the walls gives a better answer in every circumstance. However, this result is not trivial in some cases. Thermocouple MP32, located in the downstream cavity of the stator well, predicts temperature differences of up to a 1.58% compared to the non-adiabatic solution. The effect of the viscous heating is washed out by the thermal diffusion in the fluid as seen in Figure 19, which shows temperature predictions at a mid plane in the cavity for the analysis without coolant. The downstream cavity is cooler in the second (non adiabatic) case, as a result of the heat transfer between the stator foot and the cavity air. Table 3 Air temperature comparison The differences can be much more important for cooled cavity configurations with high mass flow rates. As the cavity is flooded by the coolant, the thermal gradient between the walls and the air is not negligible; hence the conduction in the fluid must be taken into account. It has been observed that the bigger the difference between the hot 8 Copyright 2010 by Rolls-Royce plc

9 gas temperature and the coolant, the bigger this effect will be. In an intermediate case in which all the coolant passes through the inter-stage seal, e.g. for 0.61% (% of main annulus flow) coolant flow, where the difference between the inlet cooling flow temperature and the walls is lower, the adiabatic wall solution gives an answer closer to the measurements. This is explained by the fact that the thermal gradients are reduced. This influence in the cavity, especially in the case of ingestion from the annulus has been identified by da Soghe [10]. This is due to an unsteady solution being required to accurately model the main annulus circumferential pressure variation at the rotor/stator rim gap. The converged steady solution was used as the initial condition for the unsteady simulation. The unsteady calculation time was similar to that required for the steady state solution to reach periodic convergence. Figure 20 plots mass flow in the main stream against time steps (two per each point in the x axis). A total of 10 periods were run with 100 time steps per period for each calculation. Adiabatic Figure 19a Air temperature contours - no coolant Non-adiabatic Figure 19b Air temperature contours - no coolant The conclusion is that the heat transfer in the walls and within the fluid plays a key role in the problem and the interaction between air and metal has to be modelled by conjugate heat transfer methods or coupled FE/CFD analysis. Comparison of Steady and Unsteady CFD Results A comparison has been conducted between steady and unsteady solutions for the rig design point, with two levels of cooling air supplied in the conventional way, via the drive-arm holes (0.61% and 1.12% cooling flow). These two cases were chosen as they were identified to be below and above the transition mass flow level between ingestion and egression at the stage 1 disc rim rear gap (see Table 2 - in the first assumption, the injected mass flow is below the inter stage seal mass flow, whereas for the higher cooling flow rate exceeds the seal leakage). The initial CFD modelling of the rig has assumed a steady solution. However, it is anticipated that an unsteady solution will be required to correctly model the ingestion of annulus gas. Figure 20 - Annulus convergence (1.12% coolant) A sensitivity analysis has been performed comparing the solution in the annulus and the cavity for both mass flow rates. The analysis in the main annulus showed that only for the cases with ingestion, do the pressure oscillations have an influence inside the cavity. The steady state solution has been compared with the mean averaged flow solution generated by HYDRA. Figure 21 shows contours of radial velocity in an axial cutting plane inside the front cavity. The contours are almost identical for the steady and un-steady solutions. Figure 22 shows a comparison of cooling or thermal effectiveness on the rear face of the stage 1 disc, between the steady and unsteady solutions at the rig design point (~10600 rpm, 1.12% cooling flow). Where cooling effectiveness is defined as: - Thot Twall CoolingEffectiveness= Thot Tcold where Twall is the adiabatic wall temperature predicted by CFD, Tcold is the inlet cooling air temperature and Thot is the mean total air temperature on a plane behind the Rotor 1 Transient exit. Any solution differences are barely noticeable. Results (steady state mean average) STEADY STATE UNSTEADY FLOW AVERAGED Figure 21 Radial velocities in the front cavity % coolant flow 9 Copyright 2010 by Rolls-Royce plc

10 Figure 22 Cooling effectiveness 1.12% The same comparison for a 0.61% coolant flow case, where ingestion is predicted, has shown different conclusions. The level of penetration of the hot gases from the annulus varies now on time and hence the mixing process within the cavity. The outer region of the upstream stator well cavity shows different temperature predictions at different time points due to local main annulus gas ingestion. This will have an effect on the metal temperatures at the stator platform, where the temperatures will be affected by this ingestion. However, at the inner part of the cavity, the flow behaviour will be dominated by the coolant supply and less affected by gas ingestion at the rim gap. This will also have consequences in the comparison between the steady state solution and the mean averaged flow, which will show bigger differences. Figure 24 Relative total temperature unsteady solution 0.61% coolant supply Figure 25 compares the ingestion case cooling effectiveness at the rear face of rotor 1 disc against radius. The effect of the ingestion is now noticeable for higher radii although much less significant for the inner part of the cavity. This unsteadiness effect also modifies the predicted interstage mass flow rate through the labyrinth seal but, as anticipated in the previous comments, by a much smaller amount, as it is within the region dominated by the coolant (see Table 4). Figure 23 Radial velocity contour plots 0.61% coolant flow case Figure 23 shows contours of radial velocity in an axial cutting plane inside the cavity at the cooling hole mid plane for the steady state and mean flow solutions. The contours are again very close at the jet region, but now show greater differences at the outer part of the cavity where, for the steady state solution, the radial velocity is lower and does not show the influence of the unsteadiness. Figure 24 compares the solution at two different time steps. The inner region keeps constant along time, as seen in the periodic contour. However, the outer area of this boundary shows a wave of temperature moving periodically on time due to the pressure variations generated by the rotor wakes. This has an effect on the stator foot and outer zone of the rotor disc where the temperature fluctuates in time periodically. Figure 25 Cooling effectiveness 0.61% flow Coolant flow case 0.61% 1.12% Interstage seal flow Steady state % % Flow averaged % % Table 4 Interstage seal flows Hence, the main conclusion is that the unsteady analysis does not produce a significant change in the answer in the cases of no ingestion from the annulus, and only a small effect if there is ingestion. The averaged flow and the steady state solution have been compared in the cavity showing small differences in cooling effectiveness in the cavity walls. 10 Copyright 2010 by Rolls-Royce plc

11 Cooling Air Mass-flow Level An investigation into the effects of cooling air mass flow level has been carried out with the multiple reference frame CFD models (steady, adiabatic solution) recognizing that there will be some quantitative limitations on the predictions of gas ingestion, but anticipating that qualitative results will give a good indication of trends. Table 5 shows the cases run during the full test matrix: Figure 28 shows rig temperature measurement locations on the rear face of the stage 1 disc. Table 5 Cooling Flow Level Investigation Figure 26 shows how thermal effectiveness on the rear face of the stage 1 disc rim varies with cooling flow level; this for the two alternative cooling flow entry locations, i.e. the conventional drive-arm holes and the lock-plate slot locations. It is evident from these predictions that the lockplate entry position requires less cooling air for a given disc rim temperature (compared with the drive-arm hole position). Also shown is a calculation of turbine stage efficiency, which shows an expected trend in reduced in stage efficiency with additional cooling air efflux. Figure 28 Temperature measurement locations Figure 29 shows a comparison of normalised temperature, θ, for a cooling air supply level of 1.12% for each of the entry points, based on the measured data. The results confirm the benefit of introducing the cooling flow at the lock-plate slot position. Figure 26 - Predicted Effect of cooling flow on Thermal Effectiveness Figure 27 shows contours of thermal effectiveness on the rear surface of the stage 1 disc rim, for a range of cooling flows (supplied at the drive arm holes from 0 to 1.84% and the lock-plate slots position from 0 to 1.43%). Figure 29 Measured Thermal Effectiveness FE-CFD linking As a further step, which also gives an indication of the future applications and ongoing work of this research, a manual coupling calculation was carried out. The test data was used to provide wall temperature boundary conditions to the Hydra CFD model at the cavity walls. From this, a number of heat flux profiles were extracted and applied to the SC03 model. This FE model was then run to the design condition with no cooling flow, providing metal temperatures in the solid domain. Figure 30 shows the test section predicted temperatures from the coupled CFD/FE solution (colour contours), compared to measured data from the rig (MPXXX). In this prediction, stator well heat fluxes calculated in the CFD solution are applied directly to the FE model. Figure 27 Thermal Effectiveness with different cooling flow levels 11 Copyright 2010 by Rolls-Royce plc

12 ACKNOWLEDGMENTS Thanks to the European Commission for support of the MAGPI research program and our university and industrial partners at The University of Florence, The University of Sussex, The University of Surrey, Avio (Italy), MTU (Germany), Siemens (UK) and Turbomeca (France). Figure 30 Test section temperature comparison Table 6 compares measured temperatures, (in a nondimensional form ), minus predicted values at the thermocouples highlighted in the figures 28 and 30. Temperature predictions are within 2% of the measured values at all locations. Table 6 CFD/FE prediction vs. measurements CONCLUSIONS Considerable progress has already been made in the MAGPI Work-package 1 partnership. A good quality set of test data is now available for the two-stage turbine and stator well cavity, covering two alternative cooling configurations and a range of cooling flow levels. The test data set also includes cooling air efflux re-ingestion data. Further data, with an optimised interstage seal geometry, will be obtained within the remaining period of the research programme. CFD and FE models of the turbine rig configuration have been produced and run to replicate the test conditions. A manual CFD/FE coupling capability has been demonstrated and results from these models have been compared with the available test data, with encouraging levels of agreement, including the prediction of component temperatures within the turbine stator well. There is more work to do, including demonstrations of fully coupled and conjugate CFD analysis, with all the relevant cavities modelled simultaneously. A further extension of the coupled CFD/FE modelling capability, to demonstrate a transient modelling capability, is confidently anticipated. This modelling capability, adequately validated by the test data from the two-stage turbine rig, will provide gas turbine engineers with the necessary tools to optimise the cooling flows to this type of component and so reduce the environmental impact of gas turbine emissions and minimise the costs of ownership. REFERENCES [1] SPECIFIC TARGETED RESEARCH PROJECT Annex I Description of Work Project acronym: MAGPI Project full title: Main Annulus Gas Path Interactions Proposal/Contract no.: Date of preparation of Annex I: May 2006 [2] Jeffrey A. Dixon, Ivan L. Brunton, Timothy J. Scanlon, Grzegorz Wojciechowski Vassilis Stefanis, Peter R. N. Childs Turbine stator well heat transfer and cooling flow optimisation ASME paper GT [3] J.Illingworth, N.Hills, C.Barnes, 3D Fluid-Solid Heat Transfer Coupling of an Aero-engine Preswirl System, ASME Gas Turbine Conference 2005 [4] Z.Sun, J.Chew, N.Hills, K.Volkov, C.Barnes, Efficient FEA/CFD thermal coupling for engineering applications, ASME Gas Turbine Conference To be published in ASME Journal of Turbomachinery. [5] D.Amirante, N.Hills, A Coupled Approach for Aerothermal Mechanical Modelling for Turbomachinery, 1st International Conference on Computational Methods for Thermal Problems, 2009 [6] Verdicchio, J. A., The validation and coupling of computational fluid dynamics and finite element codes for solving industrial problems. DPhil Thesis, University of Sussex, July [7] Edmunds T., Practical three dimensional adaptive analysis. In Proceedings of 4 th International Conference on Quality Assurance and Standards, NAFEMS, [8] FLUENT Inc. Lebanon, New Hampshire. [9] Lapworth, L. The Hydra s User Guide for version beta. Rolls-Royce plc, [10] Da Soghe, Andreini, Facchini Turbine stator well CFD studies: Effects of coolant supply geometry on cavity sealing performance, ASME TurboExpo 2009 GT [11] Launder, B.E. and Spalding, D.B., The numerical computation of turbulent flows. Comp. Meth. Appl. Mech. Eng., 1974, 3, [12] Spalart, P. R., and Allmaras, S. R., "A One-Equation Turbulence Model for Aerodynamic Flows," AIAA , 1991 [13] Coren, D. D., Atkins, N. R., Childs, P. R. N., Turner, J. R., Eastwood, D., Davies, S., Dixon, J., Scanlon, T. An Advanced Multi Configuration Turbine Stator Well Cooling Test Facility, Paper Number GT ASME, in proceedings of the ASME Turbo Expo 2010, Glasgow, UK, June Copyright 2010 by Rolls-Royce plc