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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.

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.

In a “direct-transfer” pre-swirl supply system, cooling air flows axially across the wheel-space from stationary pre-swirl nozzles to receiver holes located at a similar radius in the rotating turbine disc. This paper describes a combined computational and experimental study of the fluid dynamics of such a system. Measurements of total and static pressures have been made using a purpose-built rotor-stator rig, with 24 pre-swirl nozzles on the stator and 60 receiver holes in the rotor. The number of pre-swirl nozzles could be reduced, and it was possible to calculate CD, the discharge coefficient of the receiver holes. Information on the flowfield was also obtained from three-dimensional, incompressible steady turbulent flow computations. The measurements showed that there was a significant loss of total pressure between the outlet from the pre-swirl nozzles and the rotating core of fluid in the wheel-space. This loss increased as the pre-swirl flow-rate and inlet swirl ratio increased, and as the number of nozzles decreased. CD increased as the swirl ratio at the receiver hole radius approached unity; for the experiments, CD varied in the range 0.2 to 0.45. Computed pressures and tangential velocities were in mainly good agreement with the measurements. The computations help to explain the reasons for the significant losses in total pressure and for the relatively low values of CD in this pre-swirl system.

This paper describes experimental results from a research facility which experimentally models hot gas ingress into the wheel-space of an axial turbine stage. Measurements of CO2 gas concentration in the rim-seal region and inside the wheel-space are used to assess the performance of generic (though engine-representative) single and double seals in terms of the variation of concentration effectiveness with sealing flow rate. The variation of pressure in the turbine annulus, which governs externally-induced ingress, was obtained from steady pressure measurements downstream of the vanes.The benefit of using double seals is demonstrated: the ingested gas is shown to be predominately confined to the outer wheel-space radially outward of the inner seal; in the inner wheel-space, radially inward of the inner seal, the effectiveness is shown to be significantly higher. Criteria for ranking the performance of single and double seals are proposed, and the performance limit for any double seal is shown to be one in which the inner seal is exposed to rotationally-induced ingress.Although the ingress is a consequence of an unsteady, three-dimensional flow field and the cause-effect relationship between pressure and the sealing effectiveness is complex, the experimental data is shown to be successfully calculated by simple effectiveness equations developed from a theoretical model. The data illustrate that, for similar turbine-stage velocity triangles, the effectiveness can be correlated using two empirical parameters. In principle, these correlations could be extrapolated to a geometrically-similar turbine operating at engine-representative conditions.Copyright © 2012 by ASME

This paper describes experimental results from a research facility which experimentally models hot-gas ingress into the wheel-space of an axial turbine stage with an axial-clearance rim seal. Thermochromic liquid crystal (TLC) was used to determine the effect of ingestion on heat transfer to the rotating disc; as far as the authors are aware, this is the first time that the measured effects of ingestion on adiabatic temperature have been published. An adiabatic effectiveness for the rotor was defined, and this definition was used to determine when the effect of ingress was first experienced by the rotor. Concentration measurements on the stator were used to determine the sealing effectiveness of the rim seal, and transient heat transfer tests with heated sealing air were used to determine the adiabatic effectiveness of the rotor. The thermal buffer ratio, which is defined as the ratio of the sealing flow rate when ingress first occurs to that when it is first experienced by the rotor, was shown to depend on the turbulent flow parameter. The local Nusselt numbers, Nu, which were measured on the rotor, were significantly smaller than those for a free disc; they decreased as the sealing flow rate decreased and as the ingress correspondingly increased. The values of Nu and adiabatic effectiveness obtained in these experiments provide data for the validation of CFD codes but caution is needed if they (particularly the values of Nu) are to be extrapolated to engine conditions.Copyright © 2012 by ASME

This paper describes a new research facility which experimentally models hot gas ingestion into the wheel-space of an axial turbine stage. Measurements of the CO2 gas concentration in the rim-seal region and inside the cavity are used to assess the performance of two generic (though engine-representative) rim-seal geometries in terms of the variation of concentration effectiveness with sealing flow rate. The variation of pressure in the turbine annulus, which governs this externally-induced (EI) ingestion, was obtained from steady pressure measurements downstream of the vanes and near the rim seal upstream of the rotating blades. Although the ingestion through the rim seal is a consequence of an unsteady, three-dimensional flow field and the cause-effect relationship between the pressure and the sealing effectiveness is complex, the experimental data is shown to be successfully calculated by simple effectiveness equations developed from a previously published orifice model. The data illustrate that, for similar turbine-stage velocity triangles, the effectiveness can be correlated using a nondimensional sealing parameter, Φo. In principle, and within the limits of dimensional similitude, these correlations should apply to a geometrically-similar engine at the same operating conditions. Part II of this paper describes an experimental investigation of rotationally-induced (RI) ingress, where there is no mainstream flow and consequently no circumferential variation of external pressure.

Part I of this two-part paper presented experimental results for externally-induced (EI) ingress, where the ingestion of hot gas through the rim seal into the wheel-space of a gas turbine is controlled by the circumferential variation of pressure in the external annulus. In Part II, experimental results are presented for rotationally-induced (RI) ingress, where the ingestion is controlled by the pressure generated by the rotating fluid in the wheel-space. Although EI ingress is the common form of ingestion through turbine rim seals, RI ingress or combined ingress (where EI and RI ingress are both significant) is particularly important for double seals, where the pressure asymmetries are attenuated in the annular space between the inner and outer seals. In this paper, the sealing effectiveness was determined from concentration measurements, and the variation of effectiveness with sealing flow rate was compared with theoretical curves for RI ingress obtained from an orifice model. Using a nondimensional sealing parameter Φ0 the data could be collapsed onto a single curve, and the theoretical variation of effectiveness with Φ0 was in very good agreement with the data for a wide range of flow rates and rotational speeds. It was shown that the sealing flow required to prevent RI ingress was much less than that needed for EI ingress, and it was also shown that the effectiveness of a radial-clearance seal is significantly better than that for an axial-clearance seal for both EI and RI ingress.

In recent papers, orifice models have been developed to calculate the amount of ingestion, or ingress, that occurs through gas-turbine rim seals. These theoretical models can be used for externally-induced (EI) ingress, where the pressure differences in the main gas path are dominant, and for rotationally-induced (RI) ingress, where the effects of rotation in the wheel-space are dominant. Explicit ‘effectiveness equations’, derived from the orifice models, are used to express the flow rate of sealing air in terms of the sealing effectiveness. These equations contain two unknown terms: Φmin, a sealing flow parameter, and Γc, the ratio of the discharge coefficients for ingress and egress. The two unknowns can be determined from concentration measurements in experimental rigs. In this paper, maximum likelihood estimation is used to fit the effectiveness equations to experimental data and to determine the optimum values of Φmin and Γc. The statistical model is validated numerically using noisy data generated from the effectiveness equations, and the simulated tests show the dangers of drawing conclusions from sparse data points. Using the statistical model, good agreement between the theoretical curves and several sets of previously-published effectiveness data is achieved for both EI and RI ingress. The statistical and theoretical models have also been used to analyse previously-unpublished experimental data, the results of which are included in separate papers. It is the ultimate aim of this research to apply the effectiveness data obtained at rig conditions to engine-operating conditions.

Rotationally induced (RI) ingress is caused by the negative pressure (relative to the external air) inside the wheel-space of a gas turbine; this negative pressure, which is created by the rotating flow in the wheel-space, drives the ingestion of hot gas through the rim seals. Externally induced (EI) ingress is caused by the circumferential distribution of pressure created by the blades and vanes in the turbine annulus: Ingress occurs in those regions where the external pressure is higher than that in the wheel-space, and egress occurs where it is lower. Although EI ingress is the dominant mechanism for hot-gas ingestion in engines, there are some conditions in which RI ingress has an influence: This is referred to as combined ingress (CI). In Part I of this two-part paper, values of the sealing effectiveness (obtained using the incompressible orifice equations developed for EI ingress in an earlier paper) are compared with published experimental data and with the results obtained using 3D steady compressible computational fluid dynamics (CFD). Acceptable limits of the incompressible-flow assumption are quantified for the orifice model; For the CFD, even though the Mach number in the annulus reaches approximately 0.65, it is shown that the incompressible orifice equations are still valid. The results confirm that EI ingress is caused predominantly by the magnitude of the peak-to-trough circumferential difference of pressure in the annulus; the shape of the pressure distribution is of secondary importance for the prediction of ingress. A simple equation, derived from the orifice model, provides a very good correlation of the computed values of effectiveness. Using this correlation, it is possible to estimate the minimum sealing flow rate to prevent ingress without the need to know anything about the pressure distribution in the annulus; this makes the orifice model a powerful tool for rim-seal design.

In Part I of this two-part paper, the orifice equations were solved for the case of externally induced (EI) ingress, where the effects of rotational speed are negligible. In Part II, the equations are solved, analytically and numerically, for combined ingress (CI), where the effects of both rotational speed and external flow are significant. For the CI case, the orifice model requires the calculation of three empirical constants, including Cd,e,RI and Cd,e,EI, the discharge coefficients for rotationally induced (RI) and EI ingress. For the analytical solutions, the external distribution of pressure is approximated by a linear saw-tooth model; for the numerical solutions, a fit to the measured pressures is used. It is shown that although the values of the empirical constants depend on the shape of the pressure distribution used in the model, the theoretical variation of Cw,min (the minimum nondimensional sealing flow rate needed to prevent ingress) depends principally on the magnitude of the peak-to-trough pressure difference in the external annulus. The solutions of the orifice model for Cw,min are compared with published measurements, which were made over a wide range of rotational speeds and external flow rates. As predicted by the model, the experimental values of Cw,min could be collapsed onto a single curve, which connects the asymptotes for RI and EI ingress at the respective smaller and larger external flow rates. At the smaller flow rates, the experimental data exhibit a minimum value of Cw,min, which undershoots the RI asymptote. Using an empirical correlation for Cd,e, the model is able to predict this undershoot, albeit smaller in magnitude than the one exhibited by the experimental data. The limit of the EI asymptote is quantified, and it is suggested how the orifice model could be used to extrapolate the effectiveness data obtained from an experimental rig to engine-operating conditions.

The mainstream flow past the stationary nozzle guide vanes and rotating turbine blades in a gas turbine creates an unsteady nonaxisymmetric variation in pressure in the annulus, radially outward of the rim seal. The ingress and egress occur through those parts of the seal clearance where the external pressure is higher and lower, respectively, than that in the wheel-space; this nonaxisymmetric type of ingestion is referred to here as externally induced (EI) ingress. Another cause of ingress is that the rotating air inside the wheel-space creates a radial gradient of pressure so that the pressure inside the wheel-space can be less than that outside; this creates rotationally induced (RI) ingress, which—unlike EI ingress—can occur, even if the flow in the annulus is axisymmetric. Although the EI ingress is usually dominant in a turbine, there are conditions under which both EI and RI ingress are significant, these cases are referred to as combined ingress. In Part I of this two-part paper, the so-called orifice equations are derived for compressible and incompressible swirling flows, and the incompressible equations are solved analytically for the RI ingress. The resulting algebraic expressions show how the nondimensional ingress and egress vary with Θ0, which is the ratio of the flow rate of sealing air to the flow rate necessary to prevent ingress. It is shown that ε, the sealing effectiveness, depends principally on Θ0, and the predicted values of ε are in mainly in good agreement with the available experimental data.

Buoyancy-induced flow occurs in the rotating cavities between the adjacent discs of a gas-turbine compressor rotor. In some cases, the cavity is sealed, creating a closed system; in others, there is an axial through-flow of cooling air at the centre of the cavity, creating an open system. For the closed system, Rayleigh-Benard (R-B) flow can occur in which a series of counter-rotating vortices, with cyclonic and anti-cyclonic circulation, form in the r-φ plane of the cavity. For the open system, R-B flow can occur in the outer part of the cavity, and the core of fluid containing the vortices rotates at a slower speed than the discs: that is, the rotating core ‘slips’ relative to the discs. These flows are examples of self-organizing systems, which are found in the world of far-from-equilibrium thermodynamics and which are associated with the maximum entropy production (MEP) principle. In this paper, these thermodynamic concepts are used to explain the phenomena that have been observed in rotating cavities, and expressions for the entropy production have been derived for both open and closed systems. For the closed system, MEP corresponds to the maximisation of the heat transfer to the cavity; for the open system, it corresponds to the maximisation of the sum of the rates of heat and work transfer. Some suggestions, as yet untested, are made to show how the MEP principle could be used to simplify the computation of buoyancy-induced flows.Copyright © 2007 by ASME