# Professor Nicholas Hills

## Academic and research departments

School of Mechanical Engineering Sciences, Thermo-Fluid Systems University Technology Centre.## About

### Biography

Professor Nick Hills was the Head of Department of Mechanical Engineering Sciences until August 2021. He holds a Chair in Computational Engineering at the University of Surrey, and is also the Director of the Rolls-Royce University Technology Centre in Thermo-Fluid Systems. He previously held a Royal Academy of Engineering / Rolls-Royce Chair.

His research has focussed on CFD development, particularly for massively parallel simulations (including leading the UK Applied Aerodynamics Consortium with time on the national super-computing facilities), multi-physics models and their application to internal air systems for gas turbine engines. Research funding has been through EPSRC, InnovateUK, EU and direct industrial support.

## Publications

Better understanding and more accurate prediction of heat transfer and cooling flows in aero engine components in steady and transient operating regimes are essential to modern engine designs aiming at reduced cooling air consumption and improved engine efficiencies. This paper presents a simplified coupled transient analysis methodology that allows assessment of the aerothermal and thermomechanical responses of engine components together with cooling air mass flow, pressure and temperature distributions in an automatic fully integrated way. This is achieved by assembling a fluid network with contribution of components of different geometrical dimensions coupled to each other through dimensionally heterogeneous interfaces. More accurate local flow conditions, heat transfer and structural displacement are resolved on a smaller area of interest with multidimensional surface coupled computational fluid dynamics (CFD)/FE codes. Contributions of the whole engine air-system are predicted with a faster monodimensional flow network code. Matching conditions at the common interfaces are enforced at each time-step exactly by employing an efficient iterative scheme. The coupled simulation is performed on an industrial high pressure turbine (HPT) disk component run through a square cycle. Predictions are compared against the available experimental data. The paper proves the reliability and performance of the multidimensional coupling technique in a realistic industrial setting. The results underline the importance of including more physical details into transient thermal modeling of turbine engine components.

The paper presents a multi-disciplinary approach for aero-thermal and heat transfer analysis for internal flows. The versatility and potential benefit offered by the approach is described through the application to a realistic low pressure turbine assembly. The computational method is based on a run time code-coupling architecture that allows mixed models and simulations to be integrated together for the prediction of the sub-system aero-thermal performance. In this specific application the model is consisting of two rotor blades, the embedded vanes, the inter-stage cavity and the solid parts. The geometry represents a real engine situation. The key element of the approach is the use of a fully modular coupling strategy that aims to combine (1) flexibility for design needs, (2) variable level of modelling for better accuracy and (3) in memory code coupling for preserving computational efficiency in large system and sub-system simulations. For this particular example Reynolds Averaged Navier-Stokes (RANS) equations are solved for the fluid regions and thermal coupling is enforced with the metal (conjugate heat transfer). Fluid-fluid interfaces use mixing planes between the rotating parts while overlapping regions are exploited to link the cavity flow to the main annulus flow as well as in the cavity itself for mapping of the metal parts and leakages. Metal temperatures predicted by the simulation are compared to those retrieved from a thermal model of the engine, and the results are discussed with reference to the underlying flow physics.

The effects of surface roughness on air-riding seals are investigated here using the Rayleigh-pad as an example. Both incompressible and compressible flows are considered using both CFD analysis and analytical/numerical solutions of the Reynolds equation for various 2D or 3D roughness patterns on the stationary wall. A 'unit-based' approach for incompressible flows has also been employed and is shown to be computationally much less expensive than the full-geometry solution. Results are presented showing the effect of surface roughness on the net lift force. The effects of varying the Reynolds number are demonstrated, as well as comparative results for static stiffness.

This paper considers the coupling of a finite element thermal conduction solver with a steady, finite volume fluid flow solver. Two methods were considered for passing boundary conditions between the two codes - transfer of metal temperatures and either convective heat fluxes or heat transfer coefficients and air temperatures. These methods have been tested on two simple rotating cavity test cases and also on a more complex real engine example. Convergence rates of the two coupling methods were compared. Passing heat transfer coefficients and air temperatures was found to give the quickest convergence. The coupled method gave agreement with the analytic solution and a conjugate solution of the simple free disc problem. The predicted heat transfer results for the real engine example showed some encouraging agreement, although some modelling issues are identified. Copyright © 2001 by ASME.

Experimental measurements from a new single stage turbine are presented. The turbine has 26 vanes and 59 rotating blades with a design point stage expansion ratio of 2.5 and vane exit Mach number of 0.96. A variable sealing flow is supplied to the disc cavity upstream of the rotor and then enters the annulus through a simple axial clearance seal situated on the hub between the stator and rotor. Measurements at the annulus hub wall just downstream of the vanes show the degree of circumferential pressure variation. Further pressure measurements in the disc cavity indicate the strength of the swirling flow in the cavity, and show the effects of mainstream gas ingestion at low sealing flows. Ingestion is further quantified through seeding of the sealing air with nitrous oxide or carbon dioxide and measurement of gas concentrations in the cavity. Interpretation of the measurements is aided by steady and unsteady computational fluid dynamics solutions, and comparison with an elementary model of ingestion.

The paper describes a Large Eddy Simulation (LES) conducted for a non adiabatic rotating cavity with a radial inflow introduced from the shroud. The dimensionless mass flow rate of the radial inflow is Cw = 3500 and the rotational Reynolds number, based on the cavity outer radius, is equal to Reθ = 1.2 x 10⁶. The time averaged local Nusselt number on the heated wall is compared with the experimental data available from the literature, and with those derived from the solution of two Unsteady Reynolds Averaged Navier-Stokes (URANS) eddy viscosity models, namely the Spalart-Allmaras and the k - ω SST model. It is shown that the Nusselt number is under-predicted in the lower part of the disc and over-predicted in the outer region by both URANS models, whereas the LES provides a much better agreement with the measurements. The behaviour results primarily from a different flow structure in the source region, which, in the LES, is found to be considerably more extended and show localized buoyancy phenomena that the URANS models investigated do not capture.

Understanding and modelling of main annulus gas ingestion through turbine rim seals is considered and advanced in this paper. Unsteady 3-dimensional computational fluid dynamics (CFD) calculations and results from a more elementary model are presented and compared with experimental data previously published by Hills et al (1997). The most complete CFD model presented includes both stator and rotor in the main annulus and the inter-disc cavity. The k-ε model of turbulence with standard wall function approximations is assumed in the model which was constructed in a commercial CFD code employing a pressure correction solution algorithm. It is shown that considerable care is needed to ensure convergence of the CFD model to a periodic solution. Compared to previous models, results from the CFD model show encouraging agreement with pressure and gas concentration measurements. The annulus gas ingestion is shown to result from a combination of the stationary and rotating circumferential pressure asymmetries in the annulus. Inertial effects associated with the circumferential velocity component of the flow have an important effect on the degree of ingestion. The elementary model used is an extension of earlier models based on orifice theory applied locally around the rim seal circumference. The new model includes a term accounting for inertial effects. Some good qualitative and fair quantitative agreement with data is shown. Copyright © 2001 by ASME.

Measurements and analysis for a pre-swirl cooling air delivery system are reported here. The experimental rig used is representative of aero-engine conditions, having 18 pre-swirl nozzles, 72 receiver holes, capable of speeds up to 11 000 rpm, and giving differences between total temperature upstream of the pre-swirl nozzles and relative total temperature measured in the receiver holes of up to 26K. Pressure and temperature measurements are reported. An elementary model is developed for calculation of the cooling air delivery temperature. This accounts for the pre-swirl nozzle velocity coefficient, moments on the stationary and rotating surfaces in the pre-swirl chamber, and flows through the inner and outer seals to the chamber. The model is shown to correlate the measurements well for a range of disc speeds and pre-swirl velocity to disc speed ratios.

This paper presents numerical simulations of the unsteady flow interactions between the main annulus and the disc cavity for an axial turbine. The simulations show the influence of the main annulus asymmetries (vane wakes, blade potential effect), and the appearance of rim seal flow instabilities. The generation of secondary frequencies due to non-linear interactions is observed, and the possibility of further low frequency effects and resonance is noted. The computations are compared to experimental results, looking at tracer gas concentration and mass-flows. Results are further analysed to investigate the influence of the rim seal flow on the blading aerodynamics. The flow that is ejected through the rim seal influences the unsteady flow impinging the blades. The influence of this rim-seal flow is even observed downstream of the blades, where it distorts the radial profile of stagnation temperature. Copyright © 2006 by ASME.

The prediction of the pre-swirl cooling air delivery and disc metal temperature are important for the cooling system performance and the rotor disc thermal stresses and life assessment. In this paper, standalone 3D steady and unsteady CFD, and coupled FE-CFD calculations are presented for prediction of these temperatures. CFD results are compared with previous measurements from a direct transfer pre-swirl test rig. The predicted cooling air temperatures agree well with the measurement, but the nozzle discharge coefficients are under predicted. Results from the coupled FE-CFD analyses are compared directly with thermocouple temperature measurements and with heat transfer coefficients on the rotor disc previously obtained from a rotor disc heat conduction solution. Considering the modelling limitations, the coupled approach predicted the solid metal temperatures well. Heat transfer coefficients on the rotor disc from CFD show some effect of the temperature variations on the heat transfer coefficients. Reasonable agreement is obtained with values deduced from the previous heat conduction solution. Copyright © 2012 by ASME.

Thermal analysis of a turbine disc through a transient test cycle is demonstrated using 3D computational fluid dynamics (CFD) modeling for the cooling flow and 3D finite element analysis (FEA) for the disc. The test case is a 3D angular sector of the high pressure (HP) turbine assembly of a civil jet engine and includes details of the coolant flow around the blade roots. Proprietary FEA and CFD solvers are used to simulate the metal and fluid domains, respectively. Coupling is achieved through an iterative loop with smooth exchange of information between the FEA and CFD simulations at each time step, ensuring consistency of temperature and heat flux on the coupled interfaces between the metal and fluid domains. The coupled simulation can be completed within a few weeks using a PC cluster with multiple parallel CFD executions. The FEA/CFD coupled result agrees well with corresponding rig test data and the baseline 3D and 2D FEA solutions, which have been calibrated using test data. Provision of upstream boundary conditions and modeling of rapid transients are identified as areas of uncertainty. Averaging of CFD solutions and relaxation is used to overcome difficulties caused by CFD oscillations associated with flow unsteadiness. The present work supports the continued use and development of the FEA/CFD coupling method for industrial applications. Copyright © 2012 by ASME.

Design and optimization of an efficient internal air system of a gas turbine requires thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to numerical modelling of flow and heat transfer in a cylindrical cavity with radial inflow and comparison with the available experimental data. The simulations are carried out with axi-symmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers upto 2.1×106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart-Allmaras and the k-e , and a Reynolds stress model have been used . For cases with particularly strong vortex behaviour the eddy viscosity models show some shortcomings with the Spalart-Allmaras model giving slightly better results than the k-e model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements. Copyright © 2012 by ASME.

The paper describes the Reduced Order Modelling (ROM) for the turbulent flow in a rotor-stator cavity, a configurations commonly encountered in secondary air system of aircraft engines. The proper orthogonal decomposition (POD) that uses data from Large Eddy Simulations (LES) is here considered in order to identify a set of orthonormal basis functions for the Galerkin projection of the Navier-Stokes equations. The POD-Galerkin procedure has been validated for the relative simple turbulent shear flow of a plane Couette flow. LES statistics and experimental measurements have been used as a benchmark and overall we may claim that the models studied reasonably well predict the turbulence phenomenon for the rotor-stator flow. Two novelty are introduced in this work: (i) the extension of the estimation of the turbulent eddy viscosity proposed by Aubry et al. [1] to problems with high Reynolds numbers and rotating flows; (ii) the derivation of a nonintrusive reduced order model for turbulent rotor-stator cavity flows. (c) 2020 Elsevier Ltd. All rights reserved.

The paper presents a multidisciplinary approach for aero-thermal and heat transfer analysis for internal flows. The versatility and potential benefit offered by the approach are described through the application to a realistic low pressure turbine assembly. The computational method is based on a run time code-coupling architecture that allows mixed models and simulations to be integrated together for the prediction of the subsystem aero-thermal performance. In this specific application, the model is consisting of two rotor blades, the embedded vanes, the interstage cavity, and the solid parts. The geometry represents a real engine situation. The key element of the approach is the use of a fully modular coupling strategy that aims to combine (1) flexibility for design needs, (2) variable level of modeling for better accuracy, and (3) in memory code coupling for preserving computational efficiency in large system and subsystem simulations. For this particular example, Reynolds averaged Navier-Stokes (RANS) equations are solved for the fluid regions and thermal coupling is enforced with the metal (conjugate heat transfer, CHT). Fluid-fluid interfaces use mixing planes between the rotating parts while overlapping regions are exploited to link the cavity flow to the main annulus flow as well as in the cavity itself for mapping of the metal parts and leakages. Metal temperatures predicted by the simulation are compared to those retrieved from a thermal model of the engine, and the results are discussed with reference to the underlying flow physics.

Large-Eddy Simulations (LES) were carried out for a turbine rim seal and the sensitivity of the results to changes in grid resolution and the size of the computational domain are investigated. Ingestion of hot annulus gas into the rotor-stator cavity is compared between LES results and against experiments and Unsteady Reynolds-Averaged Navier–Stokes (URANS) calculations. The LES calculations show greater ingestion than the URANS calculation and show better agreement with experiments. Increased grid resolution shows a small improvement in ingestion predictions whereas increasing the sector model size has little effect on the results. The contrast between the different CFD models is most stark in the inner cavity, where the URANS shows almost no ingestion. Particular attention is also paid to the presence of low frequency oscillations in the disc cavity. URANS calculations show such low frequency oscillations at different frequencies than the LES. The oscillations also take a very long time to develop in the LES. The results show that the difficult problem of estimating ingestion through rim seals could be overcome by using LES but that the computational requirements were still restrictive.

Unsteady flow dynamics in turbine rim seals are known to be complex and attempts accurately to predict the interaction of the mainstream flow with the secondary air system cooling flows using computational fluid dynamics (CFD) with Reynolds-averaged Navier–Stokes (RANS) turbulence models have proved difficult. In particular, published results from RANS models have over-predicted the sealing effectiveness of the rim seal, although their use in this context continues to be common. Previous studies have ascribed this discrepancy to the failure to model flow structures with a scale greater than the one which can be captured in the small-sector models typically used. This article presents results from a series of Large-Eddy Simulations (LES) of a turbine stage including a rim seal and rim cavity for, it is believed by the authors, the first time. The simulations were run at a rotational Reynolds number Re ¼ 2.2 106 and a main annulus axial Reynolds number Rex ¼ 1.3 106 and with varying levels of coolant mass flow. Comparison is made with previously published experimental data and with unsteady RANS simulations. The LES models are shown to be in closer agreement with the experimental sealing effectiveness than the unsteady RANS simulations. The result indicates that the previous failure to predict rim seal effectiveness was due to turbulence model limitations in the turbine rim seal flow. Consideration is given to the flow structure in this region. K

Considerable progress in development and application of computational fluid dynamics (CFD) for aeroengine internal flow systems has been made in recent years. CFD is regularly used in industry for assessment of air systems, and the performance of CFD for basic axisymmetric rotor/rotor and stator/rotor disc cavities with radial throughflow is largely understood and documented. Incorporation of three-dimensional geometrical features and calculation of unsteady flows are becoming commonplace. Automation of CFD, coupling with thermal models of the solid components, and extension of CFD models to include both air system and main gas path flows are current areas of development. CFD is also being used as a research tool to investigate a number of flow phenomena that are not yet fully understood. These include buoyancy-affected flows in rotating cavities, rim seal flows and mixed air/oil flows. Large eddy simulation has shown considerable promise for the buoyancy-driven flows and its use for air system flows is expected to expand in the future.

Use of computational fluid dynamics (CFD) to model the complex, 3D disk cavity flow and heat transfer in conjunction with an industrial finite element analysis (FEA) of turbine disk thermomechanical response during a full transient cycle is demonstrated. The FEA and CFD solutions were coupled using a previously proposed efficient coupling procedure. This iterates between FEA and CFD calculations at each time step of the transient solution to ensure consistency of temperature and heat flux on the appropriate component surfaces. The FEA model is a 2D representation of high pressure and intermediate pressure (IP) turbine disks with surrounding structures. The front IP disk cavity flow is calculated using 45 deg sector CFD models with up to 2.8 million mesh cells. Three CFD models were initially defined for idle, maximum take-off, and cruise conditions, and these are updated by the automatic coupling procedure through the 13,000 s full transient cycle from stand-still to idle, maximum take-off, and cruise conditions. The obtained disk temperatures and displacements are compared with an earlier standalone FEA model that used established methods for convective heat transfer modeling. It was demonstrated that the coupling could be completed using a computer cluster with 60 cores within about 2 weeks. This turn around time is considered fast enough to meet design phase requirements, and in validation, it also compares favorably to that required to hand-match a FEA model to engine test data, which is typically several months. [DOI: 10.1115/1.4003242]

This paper describes the development of a mesh deformation method used for aero-thermo-mechanical coupling of turbo-engine components. The method is based on the nonlinear solution of an elastic medium analogy, solved using finite element discretisation and modified to let the boundary nodes be free to slide over the deflected surfaces. This sliding technique relies on a B-spline reconstruction of the moving boundary and increases the robustness of the method in situations where the boundary deflection field presents significant gradients or large relative motion between two distinct boundaries. The performance of the method is illustrated with the application to an interstage cavity of a turbine assembly, subjected to the deformations computed by a coupled thermo-mechanical analysis of the engine component.

An efficient finite element analysis/computational fluid dynamics (FEA/CFD) thermal coupling technique has been developed and demonstrated. The thermal coupling is achieved by an iterative procedure between FEA and CFD calculations. Communication between FEA and CFD calculations ensures continuity of temperature and heat flux. In the procedure, the FEA simulation is treated as unsteady for a given transient cycle. To speed up the thermal coupling, steady CFD calculations are employed, considering that fluid flow time scales are much shorter than those for the solid heat conduction and therefore the influence of unsteadiness in fluid regions is negligible. To facilitate the thermal coupling, the procedure is designed to allow a set of CFD models to be defined at key time points/intervals in the transient cycle and to be invoked during the coupling process at specified time points. To further enhance computational efficiency, a “frozen flow” or “energy equation only” coupling option was also developed, where only the energy equation is solved, while the flow is frozen in CFD simulation during the thermal coupling process for specified time intervals. This option has proven very useful in practice, as the flow is found to be unaffected by the thermal boundary conditions over certain time intervals. The FEA solver employed is an in-house code, and the coupling has been implemented for two different CFD solvers: a commercial code and an in-house code. Test cases include an industrial low pressure (LP) turbine and a high pressure (HP) compressor, with CFD modeling of the LP turbine disk cavity and the HP compressor drive cone cavity flows, respectively. Good agreement of wall temperatures with the industrial rig test data was observed. It is shown that the coupled solutions can be obtained in sufficiently short turn-around times (typically within a week) for use in design.

Unsteady flow phenomena unrelated to the main gas-path blading have been identified in a number of turbine rim seal investigations. This unsteadiness has significant influence on the sealing effectiveness predicted by the conventional steady RANS (Reynolds-averaged Navier–Stokes) method, thus it is important for turbine stage design and optimisation. This paper presents CFD (computational fluid dynamics) modelling of a chute type rim seal that has been previously experimentally investigated. The study focuses on inherent large-scale unsteadiness rather than that imposed by vanes and blades or external flow. A large-eddy simulation (LES) solver is validated for a pipe flow test case and then applied to the chute rim seal rotor/stator cavity. LES, RANS and unsteady RANS (URANS) models all showed reasonable agreement with steady measurements within the disc cavity, but only the LES shows unsteadiness at a similar distinct peak frequency to that found in the experiment, at 23 times the rotational frequency. The boundary layer profile within the chute rim seal clearance has been scrutinised, which may explain the improvement of LES over RANS predictions for the pressure drop across the seal. LES results show a clockwise mean flow vortex. A more detailed sketch of the rim sealing flow unsteady flow structures is established with the help of the LES results. However, there are some significant differences between unsteadiness predicted and the measurements, and possible causes of these are discussed.

This paper presents transient aero-thermal analysis for a gas turbine disk and the surrounding air flows through a transient slam acceleration/deceleration “square cycle” engine test, and compares predictions with engine measurements. The transient solid-fluid interaction calculations were performed with an innovative coupled finite element (FE) and computational fluid dynamics (CFD) approach. The computer model includes an aero-engine high pressure turbine (HPT) disk, adjacent structure, and the surrounding internal air system cavities. The model was validated through comparison with the engine temperature measurements and is also compared with industry standard standalone FE modelling. Numerical calculations using a 2D FE model with axisymmetric and 3D CFD solutions are presented and compared. Strong coupling between CFD solutions for different air system cavities and the FE solid model led to some numerical difficulties. These were addressed through improvement to the coupling algorithm. Overall performance of the coupled approach is very encouraging giving temperature predictions as good as a traditional model that had been calibrated against engine measurements.

The optimization of heat transfer between fluid and metal plays a crucial role in gas turbine design. An accurate prediction of temperature for each metal component can help to minimize the coolant flow requirement, with a direct reduction of the corresponding loss in the thermodynamic cycle. Traditionally, in industry fluid and solid simulations are conducted separately. The prediction of metal stresses and temperatures, generally based on finite element analysis, requires the definition of a thermal model whose reliability is largely dependent on the validity of the boundary conditions prescribed on the solid surface. These boundary conditions are obtained from empirical correlations expressing local conditions as a function of working parameters of the entire system, with validation being supplied by engine testing. However, recent studies have demonstrated the benefits of employing coupling techniques, whereby computational fluid dynamics (CFD) is used to predict the heat flux from the air to the metal, and this is coupled to the thermal analysis predicting metal temperatures. This paper describes an extension of this coupling process, accounting for the thermo-mechanical distortion of the metal through the engine cycle. Two distinct codes, a finite element analysis (FEA) solver for thermo-mechanical analysis and a finite volume solver for CFD, are iteratively coupled to produce temperatures and deformations of the solid part through an engine cycle. At each time step, the CFD mesh is automatically adapted to the FEA prediction of the metal position using efficient spring analogy methods, ensuring the continuity of the coupled process. As an example of this methodology, the cavity flow in a turbine stator well is investigated. In this test case, there is a strong link between the thermo-mechanical distortion, governing the labyrinth seal clearance, and the amount of flow through the stator well, which determines the resulting heat transfer in the stator well. This feedback loop can only be resolved by including the thermo-mechanical distortion within the coupling process

One of the key research topics in the computational fluid dynamics community is to improve the computational efficiency of steady-state finite volume codes. Real-world use cases require the solution to the Navier-Stokes equations for a wide range of Mach numbers, Reynolds numbers and mesh cell aspect ratios. This introduces stiffness in the discretised equations and therefore a slowdown in convergence. The community has pursued in particular two avenues to speed up the convergence of the corresponding error modes: Optimisation of Runge-Kutta coefficients for explicit Runge-Kutta schemes; and the introduction of implicit preconditioners, with a limited investigation of Runge-Kutta coefficients suitable to those implicit preconditioners. After proposing improvements to the implicit preconditioner, the present work proposes an optimisation procedure allowing the optimisation of the Runge-Kutta coefficients specifically for the implicit preconditioner. Employed on a realistic use case, the Runge-Kutta coefficients extracted with this method show a 20%−38% reduction of the number of iterations needed for convergence compared to Runge-Kutta coefficients recommended in the literature for comparable schemes and with the same computational cost per iteration.

This paper presents the transient aerothermal analysis of a gas turbine internal air system through an engine flight cycle featuring multiple fluid cavities that surround a HP turbine disk and the adjacent structures. Strongly coupled fluid-structure thermal interaction problems require significant computational effort to resolve nonlinearities on the interface for each time step. Simulation times may grow impractical if multiple fluid domains are included in the analysis. A new strategy is employed to decrease the cost of coupled aerothermal analysis. Significantly lower fluid domain solver invocation counts are demonstrated as opposed to the traditional coupling approach formulated on the estimates of heat transfer coefficient. Numerical results are presented using 2D finite element conduction model combined with 2D flow calculation in five separate cavities interconnected through the inlet and outlet boundaries. The coupled solutions are discussed and validated against a nominal stand-alone model. Relative performance of both coupling techniques is evaluated.

in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretisation in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretise the governing equations, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretisation. Numerical results obtained for the rotor/ stator cavity compare favourably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. The buoyancy-driven flow is simulated using the Boussinesq approximation. Predictions are compared with previous computational and experimental results. Analysis of the present results shows close correspondence to natural convection in a gravitational field and consistency with experimentally observed flow structures in a water-filled rotating annulus. Predicted mean heat transfer levels are higher than the available measurements for an air-filled rotating annulus, but in agreement with correlations for natural convection under gravity.

A direct numerical simulation of a Batchelor vortex has been carried out in the presence of freely-decaying turbulence, using both periodic and symmetric boundary conditions; the latter most closely approximates typical experimental conditions, while the former is often used in computational simulations for the purposes of numerical convenience. The higher-order velocity statistics were shown to be strongly dependent upon the boundary conditions, but the dependence could be mostly eliminated by correcting for the random, Gaussian modulation of the vortex trajectory commonly referred to as 'wandering' using a technique often employed in the analysis of experimental data. Once corrected for this wandering, the strong peaks in the Reynolds stresses normally observed at the vortex centre were replaced by smaller local extrema located within the core region but away from the centre. The distributions of the corrected Reynolds stresses suggested that the formation and organization of secondary structures within the core is the main mechanism in turbulent production during the linear growth phase of vortex development.

Previous studies have indicated some differences between steady CFD predictions of flow in a rotor-stator disc cavity with rotating bolts compared to measurements. Recently time-dependent CFD simulations have revealed the unsteadiness present in the flow and have given improved agreement with measurements. In this paper unsteady Reynolds averaged Navier-Stokes (URANS) 3600 model CFD calculations of a rotorstator cavity with rotor bolts were performed in order to better understand the flow and heat transfer within a disc cavity previously studied experimentally by other workers. It is shown that the rotating bolts generate unsteadiness due to wake shedding which creates time-dependent flow patterns within the cavity. At low throughflow conditions, the unsteady flow significantly increases the average disc temperature. A systematic parametric study is presented giving insight into the influence of number of bolts, mass flow rate, cavity gap ratio and the bolts-to-shroud gap ratio on the time depended flow within the cavity.

The paper describes a Large Eddy Simulation (LES) conducted for a non adiabatic rotating cavity with a radial inflow introduced from the shroud. The dimensionless mass flow rate of the radial inflow is Cw = 3500 and the rotational Reynolds number, based on the cavity outer radius, is equal to Req =1:2 x 106. The time averaged local Nusselt number on the heated wall is compared with the experimental data available from the literature, and with those derived from the solution of two Unsteady Reynolds Averaged Navier-Stokes (URANS) eddy viscosity models, namely the Spalart-Allmaras and the k-w SST model. It is shown that the Nusselt number is underpredicted in the lower part of the disc and over-predicted in the outer region by both URANS models, whereas the LES provides a much better agreement with the measurements. The behaviour results primarily from a different flow structure in the source region, which, in the LES, is found to be considerably more extended and show localized buoyancy phenomena that the URANS models investigated do not capture.

Better understanding and more accurate prediction of heat transfer and cooling flows in aero engine components in steady and transient operating regimes are essential to modern engine designs aiming at reduced cooling air consumption and improved engine efficiencies. This paper presents a simplified coupled transient analysis methodology that allows assessment of the aerothermal and thermomechanical responses of engine components together with cooling air mass flow, pressure and temperature distributions in an automatic fully integrated way. This is achieved by assembling a fluid network with contribution of components of different geometrical dimensions coupled to each other through dimensionally heterogeneous interfaces. More accurate local flow conditions, heat transfer and structural displacement are resolved on a smaller area of interest with multidimensional surface coupled CFD/FE codes. Contributions of the whole engine air-system are predicted with a faster mono dimensional flow network code. Matching conditions at the common interfaces are enforced at each time step exactly by employing an efficient iterative scheme. The coupled simulation is performed on an industrial high pressure turbine disk component run through a square cycle. Predictions are compared against the available experimental data. The paper proves the reliability and performance of the multidimensional coupling technique in a realistic industrial setting. The results underline the importance of including more physical details into transient thermal modelling of turbine engine components.

This paper describes a coupling framework for parallel execution of different solvers for multi-physics and multi-domain simulations with an arbitrary number of adjacent zones connected by different physical or overlapping interfaces. The coupling architecture is based on the execution of several instances of the same coupling code and relies on the use of smart edges (i.e., separate processes) dedicated to managing the exchange of information between two adjacent regions. The collection of solvers and coupling sessions forms a flexible and modular system, where the data exchange is handled by independent servers that are dedicated to a single interface connecting two solvers’ sessions. Accuracy and performance of the strategy is considered for turbomachinery applications involving Conjugate Heat Transfer (CHT) analysis and Sliding Plane (SP) interfaces.

Conjugate heat-transfer problems are typically solved using partitioned methods where fluid and solid subdomains are evaluated separately by dedicated solvers coupled through a common boundary. Strongly coupled schemes for transient analysis require fluid and solid problems to be solved many times each time step until convergence to a steady state. In many practical situations, a fairly simple and frequently employed fixed-point iteration process is rather ineffective; it leads to a large number of iterations per time step and consequently to long simulation times. In this article, Anderson mixing is proposed as a fixed-point convergence acceleration technique to reduce computational cost of thermal coupled fluid–solid problems. A number of other recently published methods with applications to similar fluid–structure interaction problems are also reviewed and analyzed. Numerical experiments are presented to illustrate relative performance of these methods on a test problem of rotating pre-swirl cavity air flow interacting with a turbine disk. It is observed that performance of Anderson mixing method is superior to that of other algorithms in terms of total iteration counts. Additional computational savings are demonstrated by reusing information from previously solved time steps.

Unsteady flow dynamics in turbine rim seals are known to be complex and attempts accurately to predict the interaction of the mainstream flow with the secondary air system cooling flows using CFD with RANS turbulence models have proved difficult. In particular, published results from RANS models have overpredicted the sealing effectiveness of the rim seal, although their use in this context continues to be common. Previous authors have ascribed this discrepancy to the failure to model flow structures with a scale greater than can be captured in the small sector models typically used. This paper presents results from a series of Large-Eddy Simulations (LES) of a turbine stage including a rim seal and rim cavity for, it is believed by the authors, the first time. The simulations were run at a rotational Reynolds number Reθ = 2.2 × 106 and a main annulus axial Reynolds number Rex = 1.3 × 106 and with varying levels of coolant mass flow. Comparison is made with previously published experimental data and with unsteady RANS simulations. The LES models are shown to be in closer agreement with the experimental sealing effectiveness than the unsteady RANS simulations. The result indicates that the previous failure to predict rim seal effectiveness was due to turbulence model limitations in the turbine rim seal flow. Consideration is given to the flow structure in this region.

Experimental measurements from a new single stage turbine are presented. The turbine has 26 vanes and 59 rotating blades with a design point stage expansion ratio of 2.5 and vane exit Mach number of 0.96. A variable sealing flow is supplied to the disc cavity upstream of the rotor and then enters the annulus through a simple axial clearance seal situated on the hub between the stator and rotor. Measurements at the annulus hub wall just downstream of the vanes show the degree of circumferential pressure variation. Further pressure measurements in the disc cavity indicate the strength of the swirling flow in the cavity, and show the effects of mainstream gas ingestion at low sealing flows. Ingestion is further quantified through seeding of the sealing air with nitrous oxide or carbon dioxide and measurement of gas concentrations in the cavity. Interpretation of the measurements is aided by steady and unsteady computational fluid dynamics solutions, and comparison with an elementary model of ingestion.

Reynolds-Averaged Navier-Stokes (RANS) computations have been conducted to investigate the ﬂow and heat trans-fer between two co-rotating discs with an axial throughﬂow of cooling air and a radial bleed introduced from the shroud. The computational ﬂuid dynamics (CFD) models have been cou-pled with a thermal model of the test rig, and the predicted metal temperature compared with the thermocouple data. CFD solutions are shown to vary from a buoyancy driven regime to a forced convection regime, depending on the radial inﬂow rate prescribed at the shroud. At a high radial inﬂow rate, the computations show an excellent agreement with the measured temperatures through a transient rig condition. At a low radial inﬂow rate, the cavity ﬂow is destabilized by the thermal stratiﬁcation. Good qualitative agreement with the measurements is shown, although a signiﬁcant over-prediction of disc temperatures is observed. This is associated with under prediction of the penetration of the axial throughﬂow into the cavity. The mismatch could be the result of strong sensitivity to the prescribed inlet conditions, in addition to possible shortcomings in the turbulence modeling.

Previous studies have indicated some differences between steady CFD predictions of flow in a rotor-stator disc cavity with rotating bolts compared to measurements. Recently time-dependent CFD simulations have revealed the unsteadiness present in the flow and have given improved agreement with measurements. In this paper unsteady Reynolds averaged Navier-Stokes (URANS) 3600 model CFD calculations of a rotor-stator cavity with rotor bolts were performed in order to better understand the flow and heat transfer within a disc cavity previously studied experimentally by other workers. It is shown that the rotating bolts generate unsteadiness due to wake shedding which creates time-dependent flow patterns within the cavity. At low throughflow conditions, the unsteady flow significantly increases the average disc temperature. A systematic parametric study is presented giving insight into the influence of number of bolts, mass flow rate, cavity gap ratio and the bolts-to-shroud gap ratio on the time depended flow within the cavity.

This paper describes Large-Eddy Simulations (LES) of the flow in a rotating cavity with narrow inter-disc spacing and a radial inflow introduced from the shroud. Simulations have been conducted using a compressible, unstructured, finite-volume solver, and testing different subgrid scale models. These include the standard Smagorinsky model with Van Driest damping function near the wall, the WALE model and the implicit LES procedure. Reynolds averaged Navier-Stokes (RANS) results, based on the Spalart-Allmaras and SST k − ω models, are also presented. LES solutions reveal a turbulent source region, a laminar oscillating core with almost zero axial and radial velocity and turbulent Ekman type boundary layers along the discs. Validations are carried out against the experimental data available from the study of Firouzian et al. [1]. It is shown that the tangential velocity and the pressure drop across the cavity are very well predicted by both RANS and LES, although significant differences are observed in the velocity profiles within the boundary layers.

A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretisation in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretise the governing equations, similarly to a finite element method, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretisation, and no subgrid modelling is included in the governing equations. Numerical results obtained for the rotor/stator cavity compare favourably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. For the buoyancy-driven flow, the energy equation is coupled to the momentum equations via the Boussinesq approximation, which has been implemented in the code considering two different formulations. Numerical predictions of the Nusselt number obtained using the traditional Boussinesq approximation are considerably higher than available experimental data. Much better agreement is obtained when the extended Boussinesq approximation is em-ployed. It is concluded that the numerical method employed has considerable potential for further investigations of rotating cavity flows.

This paper reviews the current position of five major problem areas in gas turbine secondary air system design. Although the problems are of primary interest to the designer of the coolant flow paths, since they directly affect the temperature, the stresses and thus the life of the major rotating components, three of the problems interact with the main gas path and are thus also the concern of the mainstream aerodynamicist. The five problems reviewed are: prediction of the flow distribution and heat transfer in the high pressure compressor drive cone cavity from the turbine to the rim of the HP compressor running underneath the combustion chamber; the flow penetration and heat transfer in the multiple rotating cavities formed by the multiple discs of the high pressure compressor with a rotating shaft running through the bores; the control of ingestion of hot turbine mainstream gas into the rotor-stator wheelspaces through the rim-seals; the problem of compressor and turbine stator-well heating, particularly compressor stator-wells in which excessive temperatures have been occasionally measured and finally, the pre-swirl coolant system which has to take the blade cooling air across from the stationary casing to the rotating turbine disc in the most advantageous manner.

Accurate prediction of metal temperatures, blade tip and seal clearances in high pressure compressor and turbine air systems leads to dramatic improvements in overall aero-engine efficiency and component life. Fast transients during an engine flight profile may introduce large changes in geometry between adjacent rotor and stator components. The changing dynamics in a few critical seals and interfaces can change the dynamics of the entire engine, compromising efficiency, integrity and long service life. In this paper we present results of a coupled aero-thermo-mechanical transient simulation of a high pressure turbine assembly throughout an engine flight cycle. The fluid and solid model geometry is approximated as 2D axisymmetric. The problem, formulated as a four field coupled multiphysics system of equations, is simplified using a quasi-steady state assumption: the transient thermal solid problem is coupled to a sequence of steady fluid problems and static structural problems. The predicted results compare well with the experimental measurements over the entire fluid-solid interface. We show improvement in transient predictions isolating the effects of the solid domain deformation. The remaining transient error is linked to temporal uncertainties in the fluid model inlet boundary conditions which were taken as a spatial average of the main annulus flow conditions.

Large and flexible wind turbine blades may be susceptible to severe blade deformations coupled with dynamic stall. To advance prediction capability for this problem a general deforming mesh computational fluid dynamics (CFD) method has been developed for calculating flows with moving or deforming boundaries using an elastic spring analogy. The method has been evaluated against experimental data for flow around a pitching NACA0012 airfoil in the deep dynamic stall regime where flow is highly separated, and compared with other authors0 CFD simulations for pitching airfoil. The effects of varying the reduced frequency are also investigated. During the upstroke the present results are in generally good agreement with experiment and other CFD studies. During the downstroke some differences with experiment and other CFD models are apparent. This may be due to the sensitivity of the separated flow to modelling assumptions and experimental conditions. Overall, the degree of agreement between CFD and experiment is considered encouraging.

In compressor inter-disc cavities with a central axial throughflow it is known that the flow and heat transfer is strongly affected by buoyancy in the centrifugal force field. As a step towards developing CFD methods for such flows, buoyancy-driven flows under gravity in a closed cube and under centrifugal force in a sealed rotating annulus have been studied. Numerical simulations are compared with the experimental results of Kirkpatrick and Bohn (1986) and Bohn et al (1993). Two different CFD codes have been used and are shown to agree for the stationary cube problem. Unsteady simulations for the stationary cube show good agreement with measurements of heat transfer, temperature fluctuations, and velocity fluctuations for Rayleigh numbers up to 2 × 10 . Similar simulations for the rotating annulus also show good agreement with measured heat transfer rates. The CFD results confirm Bohn et al's results, showing reduced heat transfer and a different Rayleigh number dependency compared to gravity-driven flow. Large scale flow structures are found to occur, at all Rayleigh numbers considered.

In axial gas turbines, hot air from the main annulus path tends to be ingested into the turbine disc cavities. This leads to overheating which will reduce the disc’s life time or lead to serious damage. Often, to overcome this problem, some air is extracted from the compressor to cool the rotor discs. This also helps seal the rim seals and to protect the disc from the hot annulus gas. However, this will deteriorate the overall efficiency. A detailed knowledge of the flow interaction between the main gas path and the disc cavities is necessary in order to optimise thermal effectiveness against overall efficiency due to losses of the cooling air from the main gas path. The aim of this study is to provide better understanding of the flow in a turbine stator-well, and evaluate the use of different CFD methods for this complex, 3-dimensional unsteady flow. This study presents CFD results for a 2-stage turbine. The stator-well cavity for the second row of stationary vanes is included in the calculation and results for both turbine performance and stator-well sealing efficiency are presented.

The cooling air in a rotating machine is subject to windage as it passes over the rotor surface, particularly for cases where non-axisymmetric features such as boltheads are encountered. The ability to accurately predict windage can help reduce the quantity of cooling air required, resulting in increased efficiency. Previous work has shown that steady CFD solutions can give reasonable predictions for the effects of bolts on disc moment for a rotor-stator cavity with throughflow but flow velocities and disc temperature are not well predicted. Large fluctuations in velocities have been observed experimentally in some cases. Time-dependent CFD simulations reported here bring to light the unsteady nature of the flow. Unsteady Reynolds averaged Navier-Stokes (URANS) calculations for 1200 and 3600 models of the rotor-stator cavity with 9 and 18 bolts were performed in order to better understand the flow physics. Although the rotor-stator cavity with bolts is geometrically steady in the rotating frame of reference, it was found that the bolts generate unsteadiness which creates time-dependent rotating flow features within the cavity. At low throughflow conditions, the unsteady flow significantly increases the average disc temperature.

Design of pre-swirl systems is important for the secondary air cooling system of gas turbine engines. In this paper, three pre-swirl nozzles, a cascade vane and two drilled nozzles are analysed and their performances are compared. The two drilled nozzles considered are a straight drilled nozzle and an aerodynamically designed nozzle. CFD analyses are presented for stand-alone and pre-swirl system 3D sector models at engine operating conditions near to engine maximum power condition rotational Reynolds number (Re ?) up to 4.6 ! 10 . Nozzle performance is characterised by the nozzle discharge coefficient (C ), nozzle velocity coefficient (?η) and cooling air delivery temperature. Two commonly used eddy viscosity models are employed for the study, the standard κ-ε and Spalart-Allmaras models with wall functions. Both models give very similar results for C and η and are in reasonable agreement with available experimental data. Effects of nozzle or vane number and sealing flow have been analysed. The cascade vanes perform slightly better than the aerodynamically designed drilled nozzles but the final design choice will depend on other component and manufacturing costs. An elementary model is presented to separate temperature losses due to the nozzle, stator drag and sealing flow. Copyright © 2011 by Rolls-Royce plc.

This article reports on heat transfer measurements made on a rotating test rig representing the internal disc-cone cavity of a gas turbine high-pressure (H.P.) compressor stack. Tests were carried out for a range of flow rates and rotational speeds at engine representative nondimensional conditions. The rig also had a central drive shaft, which could rotate in the same direction as the discs, contrarotate relative to the discs, or remain static. Measurements of heat transfer were obtained from a conduction solution method using measured surface temperatures as boundary conditions. Results from the outer surface of the cone are in reasonable agreement with theoretical predictions for the heat transfer from a free cone in turbulent flow. The heat transfer measurements from the inner surface of the cone reveal two regimes of heat transfer: one governed by rotation, the other by action of the throughflow. In the rotationally dominated regime, the heat transfer from the inner surface of the cone is higher for a co-rotating shaft than for either a static or contra-rotating shaft. In the throughflow-dominated regime the heat transfer shows little consistent dependence on the direction of shaft rotation. Tests carried out at different values of surface-to-fluid temperature difference add support to the hypothesis that in the rotationally dominated regime the heat transfer occurs through a process of free convection, where the buoyancy force is induced by rotation. The heat transfer from the disc is significantly lower than that from the inner surface of the cone and more or less insensitive to the sense of shaft rotation. The disc average Nusselt numbers show similar behavior to those from the inner surface of the cone and suggest that the disc heat transfer too is governed either by rotationally induced buoyancy or by the axial throughflow.

This paper presents CFD (computational fluid dynamics) modelling of a chute type rim seal that has been previously experimentally investigated. The study focuses on inherent large-scale unsteadiness rather than that imposed by vanes and blades or external flow. A large-eddy simulation (LES) solver is validated for a pipe flow test case and then applied to the chute rim seal rotor/stator cavity. LES, Reynolds-averaged Navier-Stokes (RANS) and unsteady RANS (URANS) models all showed reasonable agreement with steady measurements within the disc cavity, but only the LES shows unsteadiness at a similar distinct peak frequency to that found in the experiment, at 23 times the rotational frequency. However, there are some significant differences between unsteadiness predicted and the measurements, and possible causes of these are discussed.