Search

The radial clearance between the rotating blades and stationary casing of a gas turbine compressor depends on the radial growth of the rotating discs to which the blades are attached, and this growth depends on the buoyancy-induced flow and heat transfer in the air-filled cavities between adjacent discs. In some engines, the cavities are sealed, which creates a closed rotating cavity. A theoretical model has been developed to calculate the radial distribution of the temperature of the disc in a closed rotating cavity. The principal assumptions are that the convective heat transfer from the hot shroud to the cold hub of the cavity is via plumes of fluid in which the cold fluid moves radially outward, and the hot fluid inward, inside an inviscid quasi-axisymmetric core of rotating fluid. The fluid core is surrounded by boundary layers on all rotating surfaces, with free-convection layers on the surfaces of the shroud and hub and laminar Ekman layers on the surface of the discs. In addition to the convection, heat is transferred by one-dimensional radial conduction in the rotating discs. Using the model, equations have been derived to calculate the radial distribution of temperature in the discs and fluid core. These equations reveal that the non-dimensional temperatures for the disc and core, θd and θc, are controlled by three independent non-dimensional parameters: Reϕ, βΔT and χ, the rotational Reynolds number, the buoyancy parameter, and the compressibility parameter, respectively. The compressibility parameter is defined as χ=defMa2/βΔT where Ma is a Mach number, and χ is shown to strongly affect the radial distribution of the core temperatures. There will be a critical value of χ at which the core temperature equals that of the heated shroud. For a closed cavity with adiabatic discs and xα = 0.5, the critical value is 6.7. Above this critical value, stratification is expected to occur and heat transfer from the shroud to the core will be by conduction rather than by convection. The theoretical model predicts radial distributions of temperatures in the discs and fluid core that are in good agreement with the experimentally derived values in a companion paper.

The radial growth of compressor discs is strongly influenced by conjugate heat transfer between conduction in the co-rotating discs and buoyancy-driven convection in the rotating fluid core between the discs. An accurate prediction of metal temperatures of these discs is an important issue in thermo-mechanical design, where blade-tip clearances must be controlled carefully to ensure safety and efficiency under all operating conditions. This paper presents an experimental study of the fluid dynamics and heat transfer in a closed rotating cavity, comparing results with theoretical models and introducing a new compressibility parameter χ. At large values of χ, where compressibility effects are significant, the air temperature approaches that of the shroud; such conditions suppress buoyancy effects and the flow in the rotating cavity becomes stratified, with convection replaced by conduction inside the fluid core. There are important practical consequences of stratification with significant differences in temperature distributions and stresses inside compressor discs. The influence of χ is also shown on the radial temperature distributions for the discs and on the shroud heat transfer correlations, which are compared qualitatively with previously published data collected where the effects of compressibility are relatively small. The experiments reveal that there is a critical value of χ where the convective heat flux to the shroud is zero. The radial distribution of disc temperature was that expected from pure conduction in a cylinder. A new heat transfer correlation based on measured shroud heat flux and the theoretical core temperature is presented. The unsteady flow characteristics in the cavity were also investigated, identifying coherent rotating structures across a range of experimental conditions. These cyclonic / anti-cyclonic vortex pairs generate the non-dimensional circumferential pressure difference necessary for the radial outflow (of cold fluid) and inflow (of hot fluid) through the rotating core. The experiments show the magnitude of these pressure variations can be correlated against Grashof number and that at high values of χ the structures do not exist. The combined experimental and theoretical results will be of practical interest to engine designers and for the validation of computational models.

Diverting hazardous small bodies on impact trajectories with the Earth can in some circumstances be impossible without risking disrupting them. Disruption is a much more difficult planetary defense scenario to assess, being linked both to the response of the body to shock loading and the much more complicated gravitational dynamics of the fragments in the solar system relative to pure deflection scenarios. In this work we present a new simulation suite built on N -body gravitational methods that solves fragment orbits in the full gravitational system without recourse to more approximate methods. We assess the accuracy of our simulations and the simplifying assumptions we adopt to make the system tractable, and then discuss in more detail several specific, plausible planetary defense scenarios based on real close encounters. We find that disruption can be a very effective planetary defense strategy even for very late (sub-year) interventions, and should be considered an effective backup strategy should preferred methods, which require long warning times, fail.

A thermopile, in which a number of thermocouple junctions are arranged on either side of a thin layer of insulation, is commonly used to determine the heat flux for steady-state measurements. Gauges using this method are available commercially and a new, generic calibration method is described here. For this purpose, an equation based on physical properties has been derived to determine the theoretical relationship between the measured voltage output of the gauge and the heat flux through it. An experimental rig has been built and used to calibrate gauges under steady-state conditions for heat fluxes between 0.5 and 8 kW/m2. The gauge temperature was controlled between 30 and 110 °C, and voltage-flux correlation – based on the theoretical relationship – was determined using maximum likelihood estimation (MLE). For tests with constant gauge temperature, there was a linear relationship between the voltage and heat flux; owing to the temperature dependency of the Seebeck constants of the thermoelectric materials, the voltage increased with increasing gauge temperature. In all cases, there was very good agreement between the measured and correlated values, and the overall uncertainty of the correlation was estimated to be less than 5% of the measured heat flux.

The flow in the heated rotating cavity of an aero-engine compressor is driven by buoyancy forces, which result in pairs of cyclonic and anticyclonic vortices. The resultant cavity flow field is three-dimensional, unsteady and unstable, which makes it challenging to model the flow and heat transfer. In this paper, properties of the vortex structures are determined from novel unsteady pressure measurements collected on the rotating disc surface over a range of engine-representative parameters. These measurements are the first of their kind with practical significance to the engine designer and for validation of computational fluid dynamics. One cyclonic/anticyclonic vortex pair was detected over the experimental range, despite the measurement of harmonic modes in the frequency spectra at low Rossby numbers. It is shown that these modes were caused by unequal size vortices, with the cyclonic vortex the larger of the pair. The structures slipped relative to the discs at a speed typically around 10% to 15% of that of the rotor, but the speed of precession was often unsteady. The coherency, strength and slip of the vortex pair increased with the buoyancy parameter, due to the stronger buoyancy forces, but they were largely independent of the rotational Reynolds number.

A robust and fully predictive mathematical representation has been derived to predict the swirl ratio, pressure, and torque in enclosed rotor–stator cavities. For the flow regime of interest, turbulent boundary layers form on the rotor and stator, between which there is an inviscid fluid core. Utilizing the momentum-integral equations with suitable assumptions and the continuity of mass equation, governing equations are derived for the flow behavior, with the assumption that the swirl ratio is dependent on the radius. Predictive initial conditions are formulated, and a robust, computationally inexpensive numerical technique is implemented and predictions are shown to be in reasonable agreement with existing experimental data. The swirl ratio was proven to be highly dependent on the radius, with the distribution modified by the shroud and hub conditions. Additionally, the effects of two geometrical parameters were studied, namely, the gap ratio and non-dimensional inner radius. As the gap ratio increases from 0.05 to 0.5, the swirl ratio at the outer radius decreases from 0.56 to 0.35, leading to an increase in torque coefficient from 0.38 to 0.44. The swirl ratios for different inner radii differ at the inner part of the cavity while converging to a single value at the outer radius. The presented model can easily be integrated into the design code for gas turbine engines, contributing to the design of more efficient engines.

Buoyancy-induced flow occurs inside the rotating compressor cavities of gas turbines. These cavities are usually open at the inner radius, but in some industrial gas turbines, they are effectively closed. This paper presents measurements of the disc heat transfer and rotating flow structures in a closed cavity over a wide range of engine relevant conditions. These experimentally derived distributions of disc temperature and heat flux are the first of their kind to be published. The radial distribution of the non-dimensional disc temperature virtually collapsed onto a single curve over the full experimental range. There was a small, monotonic departure from this common curve with increasing Reynolds number; this was attributed to compressibility effects where the core temperature increases as the rotational speed increases. These results imply that, if compressibility effects are negligible, all rotating closed cavities should have a disc temperature distribution uniquely related to the geometry and disc material; this is of important practical use to the engine designer. Unsteady pressure sensors detected either three or four vortex pairs across the experimental range. The number of pairs changed with Grashof number, and the structures slipped relative to the rotating discs by less than 1% of the disc speed.

Heat transfer within the rotating compressor cavity of an aero-engine is predominantly governed by buoyancy, which can be characterized by the Grashof number. Unsteady and unstable buoyancy-induced flow structures influence the temperatures and stresses in the compressor rotors, and these affect the radial growth of the disks. In addition, the heat transfer from the disks and shroud increases the temperature of the throughflow of cooling air. This paper contains two connected parts. First, a heat transfer correlation for the shroud of a rotating cavity was determined from steady-state heat flux measurements collected in the bath compressor-cavity rig at engine-simulated conditions. The Nusselt numbers were based on the cavity air temperature adjacent to the shroud, which was predicted using the Owen–Tang buoyancy model. Heat transfer from the shroud was consistent with free convection from a horizontal plate in a gravitational field. Maximum likelihood estimation was used with a Rayleigh–Bénard equation to correlate the shroud Nusselt number with the local Grashof number. Second, an energy balance was used to calculate the enthalpy rise of the axial throughflow from the measured disk and shroud heat fluxes. Disk fluxes were derived from radial distributions of measured steady-state disk temperatures using a Bayesian model and the equations for a circular fin. The calculated throughflow temperature rise was consistent with direct thermocouple measurements. The complex, three-dimensional flow near the cavity entrance can result in enthalpy exchange penetrating upstream in the throughflow, and rotationally induced flow can create upstream axial flow in the outer part of the annulus.

The blade clearance in aero-engine compressors is mainly controlled by the radial growth of the compressor discs, to which the blades are attached. This growth depends on the radial distribution of the disc temperature, which in turn is determined by the heat transfer inside the internal rotating cavity between adjacent discs. The buoyancy-induced convection inside the cavity is significantly weaker than that associated with the forced convection in the external mainstream flow, and consequently radiation between the cavity surfaces cannot be ignored in the calculation of the disc temperatures. In this paper, both the Monte Carlo Ray-Trace (MCRT) method and the view factor (VF) method are used to calculate the radiative flux when the temperatures of the discs, shroud, and inner shaft of the compressor vary radially and axially. The Monte Carlo Ray-Trace method is computationally expensive, but it is able to incorporate the effect of complex geometries on radiation. The view factor method is quick to compute and, although the derivation becomes complicated when geometrical details are considered, it can be used as a first check of the effect of radiation in compressor cavities. Given distributions of surface temperatures, the blackbody and gray body heat fluxes were calculated for the discs, shroud, and inner shaft in two experimental compressor rigs and in a simulated compressor stage. For the experimental rigs, although the effect of radiation was relatively small for the case of large Grashof numbers, the relative effect of radiation increases as Gr (and consequently the convective heat transfer) decreases. For the simulated compressor, with a pressure ratio of 50:1 for state-of-the-art aircraft engines, radiation could have a significant effect on the disc temperature and consequently on the blade clearance; the effect is predicted to be more prominent for the next generation of aircraft engines with pressure ratios up to 70:1.

The change in compressor blade-tip clearance across the flight cycle depends on the expansion of the rotor, which in turn depends on the temperature and stress in the discs. The radial distribution of temperature is directly coupled to the buoyancy-driven flow and heat transfer in the rotating disc cavities. This paper describes a new test rig specifically designed to investigate this conjugate phenomenon. The rig test section includes four rotating discs enclosing three cavities. Two discs in the central cavity are instrumented with thermocouples to provide the radial distribution of temperature; the two outer cavities are thermally insulated to create appropriate boundary conditions for the heat transfer analysis. An axial throughflow of air is supplied between a stationary shaft and the bore of the discs. The temperature of the throughflow air is measured by thermocouples in rakes upstream and downstream of the central cavity. For a cold throughflow, the outer shroud of the central cavity is heated. Two independently-controlled radiant heaters allow differential shroud temperatures for the upstream and downstream discs, as found in aero-engine compressors. Alternatively, the throughflow can be heated above the shroud temperature to simulate the transient conditions during engine operation where stratified flow can occur inside the cavity. The rig is designed to operate in conditions where both convective and radiative heat transfer dominate; all internal surfaces of the cavity are painted matt black to allow the accurate calculation of the radiant heat transfer. Separate attachments can be fitted to the cobs of both central discs; the attachments reduce the axial gap between the cobs — reducing the gap to zero creates a closed cavity, which can occur in some compressor designs. Other instrumentation includes heat-flux gauges on the shroud and high-frequency pressure transducers embedded into the disc diaphragm to capture unsteady flow structures. Attention has been given to experimental uncertainty, including the computation of the thermal-disturbance errors, caused by thermocouples embedded in the rotating discs; a Bayesian statistical model is used to reduce the effect of uncertainties in temperature measurements on the calculation of the Nusselt number. The effect of relevant non-dimensional parameters on the radial distribution of the disc and throughflow temperatures has been shown for some typical cases.

For the next generation of aero-engines, manufacturers are planning to increase the overall compressor pressure ratio from the existing values around 50:1 to values of 70:1. The requirement to control the tight clearances between the blade tips and the casing overall engine-operating conditions is a challenge for the engine designer attempting to minimize tip-clearances losses. Accurate prediction of the tip clearance requires an accurate prediction of the radial growth of the compressor rotor, which depends on the temperature distribution of the disk. The flow in the rotating cavities between adjacent disks is buoyancy-driven, which creates a conjugate heat transfer problem: the disk temperature depends on the radial distribution of the Nusselt number, which in turn depends on the radial distribution of disk temperature. This paper focuses on calculating the radial growth of a simplified compressor disk in isolation from the other components. Calculations were performed using steady one-dimensional (1D) theoretical and two-dimensional numerical computations (2D finite element analysis (FEA)) for overall pressure ratios (OPRs) of 50:1, 60:1, and 70:1. At each pressure ratio, calculations were conducted for five different temperature distributions; the distribution based on an experimentally validated buoyancy model was used as the datum case, and the results from this were compared with those from linear, quadratic, cubic, and quartic power laws. The results show that the assumed distribution of disk temperature has a significant effect on the calculated disk growth, whereas the pressure ratio has only a relatively small effect. Good agreement between the growth calculated by the 1D theoretical model and the FEA suggests that the 1D model should be useful for design purposes. Although the results were obtained for steady-state conditions, a method is outlined for calculating the growth under transient conditions.

International audience; In 2026, the NASA Discovery mission Psyche will orbit the asteroid (16) Psyche, the largest known metal-rich asteroid in the main belt. To estimate relative ages of the surface, identify re-surfacing events and better constrain Psyche's history, impact craters will be counted and characterized. No spacecraft has ever visited a metal-rich small body; therefore, laboratory-scale impact experiments and numerical simulations will play an important role in the interpretation of the mission's data. However, the planetary applications of high-velocity impacts have so far mostly been studied for silicate targets. Limited attention has been drawn to planetary objects predominantly made of metal, and more laboratory experiments and numerical calibrations are needed. As part of this effort, we present a suite of numerical simulations using an adaptative smoothed particles hydrodynamics numerical code (ASPH) reproducing a high-velocity impact experiment conducted on a steel target. This work primarily focuses on the influence of the chosen equation of state and initial distribution of flaws in the material on the estimated crater dimensions, damage and temperature. We find that changing the EOS and initial flaw distribution affects the crater dimensions, though for a vast majority of cases the dimensions remain within 20% of the experimental values. The target is in most cases only locally weakened but not fully damaged, independently from the EOS chosen. Finally, temperatures at the impact point and around the forming crater can reach values above the melting point of iron at

The Double Asteroid Redirection Test (DART) is a NASA-sponsored mission that will be the first direct test of the kinetic impactor technique for planetary defense. The DART spacecraft will impact into Didymos-B, the moon of the binary system 65803 Didymos, and the resulting period change will be measured from Earth. Impact simulations will be used to predict the crater size and momentum enhancement expected from the DART impact. Because the specific material properties (strength, porosity, internal structure) of the Didymos-B target are unknown, a wide variety of numerical simulations must be performed to better understand possible impact outcomes. This simulation campaign will involve a large parameter space being simulated using multiple different shock physics hydrocodes. In order to understand better the behaviors and properties of numerical simulation codes applicable to the DART impact, a benchmarking and validation program using different numerical codes to solve a set of standard problems was designed and implemented. The problems were designed to test the effects of material strength, porosity, damage models, and target geometry on the ejecta following an impact and thus the momentum transfer efficiency. Several important results were identified from comparing simulations across codes, including the effects of model resolution and porosity and strength model choice: 1) momentum transfer predictions almost uniformly exhibit a larger variation than predictions of crater size; 2) the choice of strength model, and the values used for material strength, are significantly more important in the prediction of crater size and momentum enhancement than variation between codes; 3) predictions for crater size and momentum enhancement tend to be similar (within 15‐20%) when similar strength models are used in different codes. These results will be used to better design a modeling plan for the DART mission as well as to better understand the potential results that may be expected due to unknown target properties. The DART impact simulation team will determine a specific desired material parameter set appropriate for the Didymos system that will be standardized (to the extent possible) across the different codes when making predictions for the DART mission. Some variation in predictions will still be expected, but that variation can be bracketed by the results shown in this study.

The time-dependent, gray, linear radiation transport equation is discretized using the meshless local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment. The discretization includes streamline-upwind Petrov-Galerkin stabilization to prevent oscillations and improve numerical conditioning. The angular quadrature is selectively refineable to increase angular resolution in chosen directions. The time discretization is done using backward Euler. The transport solve for each direction and the solve for the scattering source are both done using Krylov iterative methods. Results indicate first-order convergence in time and second-order convergence in space for linear reproducing kernels.

For the next generation of aero-engines, manufacturers are planning to increase the overall compressor pressure ratio from existing values around 50:1 to values of 70:1. The requirement to control the tight clearances between the blade tips and the casing over all engine-operating conditions is a challenge for the engine designer attempting to minimise tip-clearances losses. Accurate prediction of the tip clearance requires an accurate prediction of the radial growth of the compressor rotor, which depends on the temperature distribution of the disc. The flow in the rotating cavities between adjacent discs is buoyancy-driven, which creates a conjugate heat transfer problem: the disc temperature depends on the radial distribution of Nusselt number, which in turn depends on the radial distribution of disc temperature. This paper focuses on calculating the radial growth of a simplified compressor disc in isolation from the other components. Calculations were performed using one-dimensional (1D) theoretical and two-dimensional finite-element computations (2D FEA) for overall pressure ratios (OPR) of 50:1, 60:1 and 70:1. At each pressure ratio, calculations were conducted for five different temperature distributions; the distribution based on an experimentally-validated buoyancy model was used as the datum case, and results from this were compared with those from linear, quadratic, cubic and quartic power laws. The results show that the assumed distribution of disc temperature has a significant effect on the calculated disc growth, whereas the pressure ratio has only a relatively small effect. The good agreement between the growth calculated by the 1D theoretical model and the FEA suggests that the 1D model should be useful for design purposes.

Understanding how a potentially hazardous object (PHO) responds to a kinetic impactor is of great interest to the planetary defense community. Target response depends upon the detailed material properties of the PHO, which may not be well constrained ahead of time. Hence, it is useful to explore a variety of target compositions for kinetic impact deflection. Previous validation efforts have focused primarily on understanding the behavior of common rocky materials, though PHOs are not exclusively composed of such material. Water ice is one material for which there has been only limited code validation against cratering experiments. It is known that comets consist of primarily icy material and some asteroids likely contain some amount of ice. Therefore, it is useful to understand the model sensitivities for ice in deflection simulations. Here we present Adaptive Smoothed Particle Hydrodynamics simulations of impacts into water ice by an aluminum projectile. We explore the sensitivities to the damage model within our code and find that the best-fit simulations of ice occur with a Weibull modulus of 12, though results can be obtained with values of the Weibull modulus near the published value of 9.59. This work demonstrates the efficacy of using an adaptive smoothed particle hydrodynamics code to simulate impacts into ice.

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the number of iterations needed to converge the emission source, and how the radiation diffusion equation is solved, which must be done in each iteration. The coupled material and radiation energy equations are solved using an inexact Newton iteration scheme based on nonlinear elimination, which reduces the number of Newton iterations needed to converge within each time step. During each Newton iteration, the radiation diffusion equation is solved using Krylov iterative methods with a multigrid preconditioner, which abstracts and optimizes much of the communication when running in parallel. The code is verified for an infinite medium problem, a one-dimensional Marshak wave, and a two and three-dimensional manufactured problem, and exhibits first-order convergence in time and second-order convergence in space. For these problems, the number of iterations needed to converge the inexact Newton scheme and the diffusion equation is independent of the number of spatial points and the number of processors.

The radiation hydrodynamics equations for smoothed particle hydrodynamics are derived by operator splitting the radiation and hydrodynamics terms, including necessary terms for material motion, and discretizing each of the sets of equations separately in time and space. The implicit radiative transfer discussed in the first paper of this series is coupled to explicit smoothed particle hydrodynamics. The result is a multi-material meshless radiation hydrodynamics code with arbitrary opacities and equations of state that performs well for problems with significant material motion. The code converges with second-order accuracy in space and first-order accuracy in time to the semianalytic solution for the Lowrie radiative shock problem and has competitive performance compared to a mesh-based radiation hydrodynamics code for a multi-material problem in two dimensions and an ablation problem inspired by inertial confinement fusion in two and three dimensions.

Ingress is the leakage of hot mainstream gas through the rim-seal clearance into the wheel-space between the rotating turbine disk (the rotor) and the adjacent stationary casing (the stator). The high-pressure rotor is purged by a radial outflow of air from the high-pressure compressor, and this cooling air is also used to reduce the ingress. The engine designer needs to predict the stator and rotor temperatures as a function of cooling-flow rate. The sealing effectiveness determines how much air is needed to reduce or prevent ingress; although there are numerous theoretical and experimental papers on the effectiveness of different seal geometries, there are few papers on the effect of ingress on the temperature of the rotating disk. This is an unsolved problem of great practical importance: under high stress, a small increase in metal temperature can significantly reduce operating life. In this paper, conservation equations and control volumes are used to develop theoretical equations for the exchange of mass, concentration and enthalpy in an adiabatic rotor–stator system when ingress occurs. It is assumed that there are boundary layers on the rotor and stator, separated by an inviscid rotating core, and the fluid entrained from the core into the boundary layer on the rotor is recirculated into that on the stator. The superposed cooling flow protects the rotor surface from the adverse effects of hot-gas ingress, which increases the temperature of the fluid entrained into the rotor boundary layer. A theoretical model has been developed to predict the relationship between the sealing effectiveness on the stator and the adiabatic effectiveness on the rotor, including the effects of both ingress and frictional heating. The model involves the use of a nondimensional buffer parameter, Ψ, which is related to the relative amount of fluid entrained into the rotor boundary layer. The analysis shows that the cooling flow acts as a buffer, which attenuates the effect of hot gas ingress on the rotor, but frictional heating reduces the buffer effect. The theoretical effectiveness curves are in good agreement with experimental data obtained from a rotor–stator heat-transfer rig, and the results confirm that the buffer effect increases as the sealing effectiveness of the rim seals decreases. The analysis quantifies the increase in the adiabatic rotor temperature due to direct frictional heating, which is separate from the increase due to the combined effects of the ingress and the indirect frictional heating of the entrained fluid. These combined effects are reduced as Ψ increases, and Ψ = 1 at a critical flow rate above which there is no entrained fluid and consequently no indirect heating of the rotor. The model also challenges the conventional physical interpretation of ingress as, in general, not all the hot gas that enters the rim-seal clearance can penetrate into the wheel-space. The ingress manifests itself through a mixing of enthalpy, which can be exchanged even if no ingested fluid enters the wheel-space.

In gas turbines, rim seals are fitted at the periphery of stator and rotor discs to minimise the purge flow required to seal the wheel-space between the discs. Ingestion (or ingress) of hot mainstream gases through rim seals is a threat to the operating life and integrity of highly-stressed components, particularly in the first-stage turbine. Egress of sealing flow from the first-stage can be re-ingested in downstream stages. This paper presents experimental results using a 1.5-stage test facility designed to investigate ingress into the wheel-spaces upstream and downstream of a rotor disc. Re-ingestion was quantified using measurements of CO2 concentration, with seeding injected into the upstream and downstream sealing flows. Here a theoretical mixing model has been developed from first principles and validated by the experimental measurements. For the first time, a method to quantify the mass fraction of the fluid carried over from upstream egress into downstream ingress has been presented and measured; it was shown that this fraction increased as the downstream sealing flow rate increased. The upstream purge was shown to not significantly disturb the fluid dynamics but only partially mixes with the annulus flow near the downstream seal, with the ingested fluid emanating from the boundary layer on the blade platform. From the analogy between heat and mass transfer, the measured mass-concentration flux is equivalent to an enthalpy flux and this re-ingestion could significantly reduce the adverse effect of ingress in the downstream wheel-space. Radial traverses using a concentration probe in and around the rim seal clearances provide insight into the complex interaction between the egress, ingress and mainstream flows.

The buoyancy-induced flow and heat transfer inside the compressor rotors of gas-turbine engines affects the stresses and radial growth of the compressor disks, and it also causes a temperature rise in the axial throughflow of cooling air through the center of the disks. In turn, the radial growth of the disks affects the radial clearance between the rotating compressor blades and the surrounding stationary casing. The calculation of this clearance is extremely important, particularly in aeroengines where the increase in pressure ratios results in a decrease in the size of the blades. In this paper, a published theoretical model—based on buoyancy-induced laminar Ekman-layer flow on the rotating disks—is extended to include laminar free convection from the compressor shroud and forced convection between the bore of the disks and the axial throughflow. The predicted heat transfer from these three surfaces is then used to calculate the temperature rise of the throughflow. The predicted temperatures and Nusselt numbers are compared with measurements made in a multicavity compressor rig, and mainly good agreement is achieved for a range of Rossby, Reynolds, and Grashof numbers representative of those found in aeroengine compressors. Owing to compressibility effects in the fluid core between the disks—and as previously predicted—increasing rotational speed can result in an increase in the core temperature and a consequent decrease in the Nusselt numbers from the disks and shroud.

The cavities between the rotating compressor discs in aeroengines are open, and there is an axial throughflow of cooling air in the annular space between the centre of the discs and the central rotating compressor shaft. Buoyancy-induced flow occurs inside these open rotating cavities, with an exchange of heat and momentum between the axial throughflow and the air inside the cavity. However, even where there is no opening at the centre of the compressor discs — as is the case in some industrial gas turbines — buoyancy-induced flow can still occur inside the closed rotating cavities. The closed cavity also provides a limiting case for an open cavity when the axial clearance between the cobs — the bulbous hubs at the centre of compressor discs — is reduced to zero. Bohn and his co-workers at the University of Aachen have studied three different closed-cavity geometries, and they have published experimental data for the case where the outer cylindrical surface is heated and the inner surface is cooled. In this paper, a buoyancy model is developed in which it is assumed that the heat transfer from the cylindrical surfaces is analogous to laminar free convection from horizontal plates, with the gravitational acceleration replaced by the centripetal acceleration. The resulting equations, which have been solved analytically, show how the Nusselt numbers depend on both the geometry of the cavity and its rotational speed. The theoretical solutions show that compressibility effects in the core attenuate the Nusselt numbers, and there is a critical Reynolds number at which the Nusselt number will be a maximum. For the three cavities tested, the predicted Nusselt numbers are in generally good agreement with the measured values of Bohn et al. over a large range of Raleigh numbers up to values approaching 1012. The fact that the flow remains laminar even at these high Rayleigh numbers is attributed to the Coriolis accelerations suppressing turbulence in the cavity, which is consistent with recently-published results for open rotating cavities.

Calculation of the clearances between the blades and casing of the high-pressure-compressor rotors in aeroengines involves calculating the radial growth of the corotating compressor disks. This requires the calculation of the thermal growth of the disks, which in turn requires knowledge of their temperatures and of the Nusselt numbers and the flow structure in the cavity between the disks. The authors have recently published a theoretical model of the buoyancy-induced flow in rotating cavities, and approximate solutions were obtained for laminar Ekman-layer flow on the disks; the equation for the Nusselt numbers, which includes two empirical constants, depends strongly on the Grashof number and on the radial distribution of disk temperature. In this paper, Nusselt numbers and disk temperatures predicted by the buoyancy model are compared with values obtained from published experimental data. For most of the 19 test cases, with Grashof numbers up to nearly 1012, mainly good agreement was achieved between the theoretical and experimental distributions of Nusselt numbers and disk temperatures. This suggests that, owing to Coriolis effects, the laminar model of buoyancy-induced rotating flow could be valid even at the high Grashof numbers found in the compressor rotors of aeroengines. As predicted by the model, for a constant Grashof number increasing the rotational Reynolds number can cause a decrease in the Nusselt number. This is the first time a theoretical model (rather than computational fluid dynamics (CFD)) has been used to predict the temperatures of a compressor disk, and the model takes only seconds to predict disk temperatures that would take days or even weeks to predict using CFD. More experimental data is required if the model is to be used by the designers of compressor rotors, and suggestions for future research are given in the paper.

We describe new methods of computing post-remap nodal and subzonal masses in Arbitrary Lagrangian Eulerian (ALE) calculations employing the staggered energy conserving Lagrangian hydrodynamics method of Caramana et al. (1998) [12]. An important feature of this Lagrangian algorithm is the distribution of the masses to subzonal corners within each zone, which is then used to difference the momentum and energy equations such that both linear momentum and total energy are conserved. Such algorithms present challenges when employed as part of an ALE application, however, as these subzonal masses must be treated consistently through the remap phase. In this work we develop new ideas to compute the post-remap corner masses and associated mass fluxes between the nodal control volumes, such that the new corner masses (and therefore zonal and nodal masses) are consistently defined and conservation of linear momentum is ensured through the ALE step. We demonstrate applications of these ideas on examples including pure remapping and full ALE test cases.

SUMMARY We describe a modified form of smoothed particle hydrodynamics (SPH) in which the specific thermal energy equation is based on a compatibly differenced formalism, guaranteeing exact conservation of the total energy. We compare the errors and convergence rates of the standard and compatible SPH formalisms on a variety of shock test problems with analytic answers. We find that the new compatible formalism reliably achieves the expected first-order convergence for these analytic shock tests and, in all cases, improves the accuracy of the numerical solution over the standard formalism. We also examine the performance of our new formalism on a more complicated applied problem: the diversion of an asteroid by a kinetic impactor. We find the compatible discretization demonstrates measurable improvement in the convergence of properties such as the deflection velocity in this kind of applied problem as well. Copyright © 2014 John Wiley & Sons, Ltd.

This paper discusses the flow structure in typical rotor–stator systems with ingress and egress. Measurements of concentration, velocity and pressure were made using a rotating-disc rig which experimentally simulated hot gas ingestion into the wheel-space of an axial turbine stage. Externally-induced ingress through rim seals was generated from the non-axisymmetric pressures produced by the flow over the vanes and blades in the external annulus. Measurements were conducted using several single- and double-seal geometries and for a range of sealing flow rates and rotational speeds. The concentration measurements showed that the amount of ingress, which increased with decreasing sealing flow rate, depended on the seal geometry. The swirl velocity in the fluid core increased with decreasing sealing-flow rate, but outside the outer region in the wheel-space, it was largely unaffected by the seal geometry or by the amount of ingress. The radial distribution of static pressure, calculated from the measured swirl velocity in the core, was in good agreement with the pressures measured on the stator. The data for the double seals demonstrated that the ingested gas was predominately confined to the region between the seals near the periphery of the wheel-space; in the inner wheel-space, the effectiveness is shown to be significantly higher. The results are of direct relevance to the engine designer who uses complex rim seals often designed through computational fluid dynamics. The designer needs to know how much sealing air is required to prevent ingress, what is the effect of ingress on metal temperature and stresses, and how these factors are governed by the flow structure in the wheel-space.

This paper describes results obtained from an experimental facility, which models ingress through the rim seal into the upstream wheel-space of an axial-turbine stage. The experimental rig included 32 nozzle guide vanes and 41 symmetrical turbine blades, and the paper presents measurements of ɛ (the sealing effectiveness) for single- and double-clearance seals for both over-speed (where the blades rotate faster than at the design point) and under-speed conditions. The design flow coefficient was CF = 0.538, and tests were conducted for 0 F F that was in mainly good agreement with the theoretical curve for combined ingress, which covered the transition from rotationally-induced to externally-induced ingress. Departure of the measured values of [Formula: see text] from the combined ingress curve occurred at very low values of CF for all the seals tested; this was attributed to the effects of separation of the mainstream flow over the turbine blades at large ‘deviation angles’ between the flow and the blades. The measurements are expected to be qualitatively similar to but quantitatively different from those experienced in engines.

Stickney crater, at 9 km across, dominates the morphology of ~22-km Phobos, the larger of the two moons of Mars. The Stickney impact event had global repercussions for Phobos, including extensive resurfacing and fracturing of the moon. Understanding the initial conditions and dynamical consequences of the collision is necessary to test competing hypotheses for the origin of peculiar grooved terrain that striates much of the surface. Previous modeling of the impact event was unable to replicate Stickney without globally fragmenting the satellite. Here we describe high-resolution numerical simulations that successfully generate Stickney crater while maintaining the large-scale structure of Phobos. Target porosity, which is estimated to be significant, aids in keeping the moon intact. Damage follows patterns centered on Stickney that are inconsistent with the observed alignment of grooved terrain on Phobos. Low-velocity boulders are ejected at shallow angles in sufficient numbers to support a rolling-boulder origin for grooved terrain.

Here we present three-dimensional high resolution simulations of Type Ia supernova in the presence of a non-degenerate companion. We find that the presence of a nearby companion leaves a long-lived hole in the supernova ejecta. In particular, we aim to study the long term evolution of this hole as the supernova ejecta interacts with the surrounding interstellar medium. Using estimates for the x-ray emission, we find that the hole generated by the companion remains for many centuries after the interaction between the ejecta and the interstellar medium. We also show that the hole is discernible over a wide range of viewing angles and companion masses., 12 pages, 14 figures, accepted to ApJ

In gas turbines, hot mainstream flow can be ingested into the wheel-space formed between stator and rotor disks as a result of the circumferential pressure asymmetry in the annulus; this ingress can significantly affect the operating life, performance, and integrity of highly stressed, vulnerable engine components. Rim seals, fitted at the periphery of the disks, are used to minimize ingress and therefore reduce the amount of purge flow required to seal the wheel-space and cool the disks. This paper presents experimental results from a new 1.5-stage test facility designed to investigate ingress into the wheel-spaces upstream and downstream of a rotor disk. The fluid-dynamically scaled rig operates at incompressible flow conditions, far removed from the harsh environment of the engine which is not conducive to experimental measurements. The test facility features interchangeable rim-seal components, offering significant flexibility and expediency in terms of data collection over a wide range of sealing flow rates. The rig was specifically designed to enable an efficient method of ranking and quantifying the performance of generic and engine-specific seal geometries. The radial variation of CO2 gas concentration, pressure, and swirl is measured to explore, for the first time, the flow structure in both the upstream and downstream wheel-spaces. The measurements show that the concentration in the core is equal to that on the stator walls and that both distributions are virtually invariant with radius. These measurements confirm that mixing between ingress and egress is essentially complete immediately after the ingested fluid enters the wheel-space and that the fluid from the boundary layer on the stator is the source of that in the core. The swirl in the core is shown to determine the radial distribution of pressure in the wheel-space. The performance of a double radial-clearance seal is evaluated in terms of the variation of effectiveness with sealing flow rate for both the upstream and the downstream wheel-spaces and is found to be independent of rotational Reynolds number. A simple theoretical orifice model was fitted to the experimental data showing good agreement between theory and experiment for all cases. This observation is of great significance as it demonstrates that the theoretical model can accurately predict ingress even when it is driven by the complex unsteady pressure field in the annulus upstream and downstream of the rotor. The combination of the theoretical model and the new test rig with its flexibility and capability for detailed measurements provides a powerful tool for the engine rim-seal designer.

This review summarizes research concerned with the ingress of hot mainstream gas through the rim seals of gas turbines. It includes experimental, theoretical, and computational studies conducted by many institutions, and the ingress is classified as externally induced (EI), rotationally induced (RI), and combined ingress (CI). Although EI ingress (which is caused by the circumferential distribution of pressure created by the vanes and blades in the turbine annulus) occurs in all turbines, RI and CI ingress can be important at off-design conditions and for the inner seal of a double-seal geometry. For all three types of ingress, the equations from a simple orifice model are shown to be useful for relating the sealing effectiveness (and therefore the amount of hot gas ingested into the wheel-space of a turbine) to the sealing flow rate. In this paper, experimental data obtained from different research groups have been transformed into a consistent format and reviewed using the orifice model equations. Most of the published results for sealing effectiveness have been made using concentration measurements of a tracer gas (usually CO2) on the surface of the stator, and—for a large number of tests with single and double seals—the measured distributions of effectiveness with sealing flow rate are shown to be consistent with those predicted by the model. Although the flow through the rim seal can be treated as inviscid, the flow inside the wheel-space is controlled by the boundary layers on the rotor and stator. Using boundary-layer theory and the similarity between the transfer of mass and energy, a theoretical model has been developed to relate the adiabatic effectiveness on the rotor to the sealing effectiveness of the rim seal. Concentration measurements on the stator and infrared (IR) measurements on the rotor have confirmed that, even when ingress occurs, the sealing flow will help to protect the rotor from the effect of hot-gas ingestion. Despite the improved understanding of the “ingress problem,” there are still many unanswered questions to be addressed.

This paper describes a new method to determine the heat transfer coefficient, h , and the adiabatic-surface temperature, T ad , from transient measurements of the surface temperature of a test piece. Maximum Likelihood Estimation (MLE) is used in conjunction with Fourier’s 1D equation to determine the optimum values of h and T ad , and also their 95% confidence intervals, without having to measure the air temperature. Validation experiments are conducted in a small purpose-built wind tunnel, and a novel infra-red (IR) sensor is used to measure the surface temperature of the test piece. A mesh heater is used to generate either a step-change in the air temperature or a ‘slow-transient’ in which the air temperature – and consequently T ad – increases slowly with time. Numerical simulations, using ‘noisy data’, show that the computations give accurate estimates of h and T ad for both the step-change and slow-transient cases. The values of h and T ad determined from the measurements in the wind-tunnel are in good agreement with empirical correlations for turbulent flow over a flat plate. An advantage of the new method is that it can be used for all transient experiments, even those slow transients that violate the assumption of a semi-infinite solid, an assumption that is used in most existing analysis methods. The new method, which was applied here to boundary-layer flow with one stream of fluid, could also be applied to ‘three-temperature problems’, like film cooling, which involve two streams of fluid. The significant advantage of using the method for these problems is that both h and T ad could be determined accurately from a single experiment.

In gas turbines, hot mainstream flow can be ingested into the wheel-space formed between stator and rotor discs as a result of the circumferential pressure asymmetry in the annulus; this ingress can significantly affect the operating life, performance and integrity of highly-stressed, vulnerable engine components. Rim seals, fitted at the periphery of the discs, are used to minimise ingress and therefore reduce the amount of purge flow required to seal the wheel-space and cool the discs. This paper presents experimental results from a new 1.5-stage test facility designed to investigate ingress into the wheel-spaces upstream and downstream of a rotor disc. The fluid-dynamically-scaled rig operates at incompressible flow conditions, far removed from the harsh environment of the engine which is not conducive to experimental measurements. The test facility features interchangeable rim-seal components, offering significant flexibility and expediency in terms of data collection over a wide range of sealing-flow rates. The rig was specifically designed to enable an efficient method of ranking and quantifying the performance of generic and engine-specific seal geometries. The radial variation of CO2 gas concentration, pressure and swirl is measured to explore, for the first time, the flow structure in both the upstream and downstream wheel-spaces. The measurements show that the concentration in the core is equal to that on the stator walls and that both distributions are virtually invariant with radius. These measurements confirm that mixing between ingress and egress is essentially complete immediately after the ingested fluid enters the wheel-space and that the fluid from the boundary-layer on the stator is the source of that in the core. The swirl in the core is shown to determine the radial distribution of pressure in the wheel-space. The performance of a double radial-clearance seal is evaluated in terms of the variation of effectiveness with sealing flow rate for both the upstream and the downstream wheel-spaces and is found to be independent of rotational Reynolds number. A simple theoretical orifice model was fitted to the experimental data showing good agreement between theory and experiment for all cases. This observation is of great significance as it demonstrates that the theoretical model can accurately predict ingress even when it is driven by the complex unsteady pressure field in the annulus upstream and downstream of the rotor. The combination of the theoretical model and the new test rig with its flexibility and capability for detailed measurements provides a powerful tool for the engine rim-seal designer.

Calculation of the clearances between the blades and casing of the high-pressure-compressor rotors in aeroengines involves calculating the radial growth of the corotating compressor discs. This requires the calculation of the thermal growth of the discs, which in turn requires a knowledge of their temperatures and of the Nusselt numbers and the flow structure in the cavity between the discs. The authors have recently published a theoretical model of the buoyancy-induced flow in rotating cavities, and approximate solutions were obtained for laminar Ekman-layer flow on the discs; the equation for the Nusselt numbers, which includes two empirical constants, depends strongly on the Grashof number and on the radial distribution of disc temperature. In this paper, Nusselt numbers and disc temperatures predicted by the buoyancy model are compared with values obtained from published experimental data. For most of the 19 test cases, with Grashof numbers up to nearly 1012, mainly good agreement was achieved between the theoretical and experimental distributions of Nusselt numbers and disc temperatures. This suggests that, owing to Coriolis effects, the laminar model of buoyancy-induced rotating flow could be valid even at the high Grashof numbers found in the compressor rotors of aeroengines. As predicted by the model, for a constant Grashof number increasing the rotational Reynolds number can cause a decrease in the Nusselt number. This is the first time a theoretical model (rather than CFD) has been used to predict the temperatures of a compressor disc, and the model takes only seconds to predict disc temperatures that would take days or even weeks to predict using CFD. More experimental data is required if the model is to be used by the designers of compressor rotors, and suggestions for future research are given in the paper.

We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using reproducing kernel (RK) interpolation have had difficulties maintaining conservation of momentum due to the fact the RK kernels are not, in general, spatially symmetric. Here, we utilize a reformulation of the fluid equations such that mass, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation. Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation. Additionally, by exploiting the increased accuracy of the RK method's gradient, we formulate a simple limiter for the artificial viscosity that reduces the excess diffusion normally incurred by the ordinary SPH artificial viscosity. Collectively, we call our suite of modifications to the traditional SPH scheme Conservative Reproducing Kernel SPH, or CRKSPH. CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomings of SPH, particularly the overly aggressive artificial viscosity and zeroth-order inaccuracy. We compare CRKSPH to two different modern SPH formulations (pressure based SPH and compatibly differenced SPH), demonstrating the advantages of our new formulation when modeling fluid mixing, strong shock, and adiabatic phenomena.

We discuss a generalization of the classic Keplerian disk test problem allowing for both pressure and rotational support, as a method of testing astrophysical codes incorporating both gravitation and hydrodynamics. We argue for the inclusion of pressure in rotating disk simulations on the grounds that realistic, astrophysical disks exhibit non-negligible pressure support. We then apply this test problem to examine the performance of various smoothed particle hydrodynamics (SPH) methods incorporating a number of improvements proposed over the years to help SPH better address problems noted in modeling the classical gravitation only Keplerian disk. We also apply this test to a newly developed extension of SPH based on reproducing kernels called CRKSPH. Counterintuitively, we find that pressure support worsens the performance of traditional SPH on this problem, causing unphysical collapse away from the steady-state disk solution even more rapidly than the purely gravitational problem, whereas CRKSPH greatly reduces this error., Comment: 13 pages, 12 figures, ApJ in review

Three-dimensional unsteady computational fluid dynamics is applied to the ingestion of fluid from a non-uniform mainstream annulus flow via a rim-seal into a rotor-stator wheel-space. The results provide understanding of the complex flow and information for the development of more efficient computational models and analytical ‘orifice models’. The commercial computational fluid dynamics code CFX has been used to carry out unsteady Reynolds-averaged Navier–Stokes computations with an shear stress transport turbulence model. A scalar equation is employed to represent the seeded tracer gas that can be used in experiments to determine sealing effectiveness, and the variation of effectiveness with sealing flow rate is determined for a simple axial clearance seal and one combination of axial and rotational Reynolds numbers. The computational domain comprises one pitch in a row of stator vanes and rotor blades. The rotating blade is accounted for by a sliding interface between the stationary and rotating sections of the model, located downstream of the seal clearance. The unsteady computations confirm that the magnitude of the peak-to-trough pressure difference in the annulus is the principal driving mechanism for ingestion (or ingress) into the wheel-space. This pressure difference is used in orifice models to predict sealing effectiveness; its magnitude however depends on the locations in the annulus and the wheel-space that are chosen for its evaluation as well as the sealing flow rate. The computational fluid dynamics is used to investigate the appropriateness of the locations that are often used to determine the pressure difference. It is shown that maximum ingestion occurs when the static pressure peak produced by the vane combines with that produced by the blade, and that highly swirled ingested flow could contact both the stator and rotor disk when little sealing flow is provided. The relationships between the unsteady simulations and simplified, more computationally efficient steady computations are also investigated. For the system considered here, ingress is found to be dictated principally by the pressure distribution caused by the vane. The effect of the rotating blade on the pressure distribution in the annulus is investigated by comparing the unsteady results with those for steady models that do not involve a blade. It is found that the presence of the blade increases the pressure asymmetry in the annulus. Although the pressure asymmetry predicted by unsteady and steady models have a similar magnitude, the sealing effectiveness is over-predicted considerably for the corresponding steady model. If a ‘thin seal’ geometric approximation is used in the steady model, however, similar effectiveness results compared with the unsteady model may be obtained much more economically.

Buoyancy-induced flow can occur in the cavity between the co-rotating compressor discs in gas-turbine engines, where the Rayleigh numbers can be in excess of 1012. In most cases the cavity is open at the centre, and an axial throughflow of cooling air can interact with the buoyancy-induced flow between the discs. Such flows can be modeled, computationally and experimentally, by a simple rotating cavity with an axial flow of air. This paper describes work conducted as part of ICAS-GT, a major European research project. Experimental measurements of velocity, temperature and heat transfer were obtained on a purpose-built experimental rig, and these results have been reported in an earlier paper. In addition, 3D unsteady CFD computations were carried out using a commercial code (Fluent) and an RNG k-ε turbulence model. The computed velocity vectors and contours of temperature reveal a flow structure in which, as seen by previous experimenters, ‘radial arms’ transport cold air from the centre to the periphery of the cavity, and regions of cyclonic and anti-cyclonic circulation are formed on either side of each arm. The computed radial distribution of the tangential velocity agrees reasonably well with the measurements in two of the three cases considered here. In the third case, the computations significantly over-predict the measurements; the reason for this is not understood. The computed and measured values of Nu for the heated disc show qualitatively similar radial distributions, with high values near the centre and the periphery. In two of the cases, the quantitative agreement is reasonably good; in the third case, the computations significantly under-predict the measured values.

The ingress of hot gas through the rim seal of a gas turbine depends on the pressure difference between the mainstream flow in the turbine annulus and that in the wheel-space radially inward of the seal. This paper describes experimental measurements which quantify the effect of ingress on both the stator and rotor discs in a wheel-space pressurised by sealing flow. Infrared sensors were developed and calibrated to accurately measure the temperature history of the rotating disc surface during a transient experiment, leading to an adiabatic effectiveness. The performance of four generic (though engine-representative) single- and double-clearance seals was assessed in terms of the variation of adiabatic effectiveness with sealing flow rate. The measurements identify a so-called thermal buffering effect, where the boundary layer on the rotor protects the disc from the effects of ingress. It was shown that the effectiveness on the rotor was significantly higher than the equivalent stator effectiveness for all rim seals tested. Although the ingress through the rim seal is a consequence of an unsteady, three-dimensional flow field, and the cause-effect relationship between pressure and the sealing effectiveness is complex, the time-averaged experimental data is shown to be successfully predicted by relatively simple semi-empirical models, which are described in a separate paper. Of particular interest to the designer, significant ingress can enter the wheel-space before its effect is sensed by the rotor.Copyright © 2015 by ASME

Sealing air is used in gas turbines to reduce the amount of hot gas that is ingested through the rim seals into the wheel-space between the turbine disk and its adjacent stationary casing. The sealing air attaches itself to the rotor, creating a buffering effect that reduces the amount of ingested fluid that can reach the surface of the rotor. In this paper, a theoretical model is developed, and this shows that the maximum buffering effect occurs at a critical flow rate of sealing air, the value of which depends on the seal geometry. The model, which requires two empirical constants, is validated using experimental data, obtained from infrared (IR) temperature measurements, which are presented in a separate paper. There is good agreement between the adiabatic effectiveness of the rotor estimated from the model and that obtained from the IR measurements. Of particular interest to designers is that significant ingress can enter the wheel-space before its effect is sensed by the rotor.

Calculation of the blade tip clearances of the high-pressure-compressor rotors in aeroengines involves calculating the radial growth of the corotating compressor discs. This requires the calculation of the thermal growth of the discs, which in turn requires a knowledge of the disc temperatures and Nusselt numbers for the buoyancy-induced flow in the cavity between the discs. This is a strongly conjugate problem in which the equations for the fluid flow and the disc temperature are coupled. In this thesis, the buoyancy-induced flow and heat transfer inside the compressor rotors is modelled assuming laminar Ekman-layer flow on the discs and compressible flow in the fluid core between the Ekman layers; conduction in the discs is modelled using a one-dimensional fin equation. The theoretical predictions are compared with Nusselt numbers and temperatures obtained from two independent sets of temperature measurements, obtained on a multi-cavity compressor rig, and the ‘experimental’ Nusselt numbers were calculated using a Bayesian model for the inverse solution of the fin equation. For most of the experimental cases, with Grashof numbers up to 1012, mainly good agreement was achieved between the theoretical predictions and experimental values of the disc temperatures and Nusselt numbers. As predicted by the model, increasing the rotational Reynolds number can, under certain conditions, cause a decrease in the Nusselt numbers. Importantly, the results suggest that laminar Ekman-layer flow could occur even at the high Grashof numbers found in the compressor rotors of aeroengines. An extension of the buoyancy model included empirical correlations for the Nusselt numbers for the compressor shroud and disc cobs. This extended model was used to predict the temperature rise of the axial throughflow of cooling air in the compressor rotor, and reasonable agreement was achieved between the predicted and measured throughflow temperatures. This is the first time a theoretical model (rather than CFD) has been used to predict the temperatures of a compressor disc and the axial throughflow, and the model takes only seconds to predict the temperatures that would take days or even weeks to predict using CFD. Some suggestions are made for future research to improve the extent and accuracy of the model.

Sealing air is used in gas turbines to reduce the amount of hot gas that is ingested through the rim seals into the wheel-space between the turbine disc and its adjacent stationary casing. The sealing air attaches itself to the rotor, creating a buffering effect that reduces the amount of ingested fluid that can reach the surface of the rotor. In this paper, a theoretical model is developed, and this shows that the maximum buffering effect occurs at a critical flow rate of sealing air, the value of which depends on the seal geometry. The model, which requires two empirical constants, is validated using experimental data, obtained from infra-red (IR) temperature measurements, which are presented in a separate paper. There is good agreement between the adiabatic effectiveness of the rotor estimated from the model and that obtained from the IR measurements. Of particular interest to designers is that significant ingress can enter the wheel-space before its effect is sensed by the rotor.