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A cross section through a high pressure aero-engine compressor. Reprinted with permission from Owen et al., Aerospace 5(1), 32, 2018. Copyright 2018 Author(s), licensed under a Creative Commons Attribution (CC BY) license.
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Future gas turbine engines require improved understanding of the heat transfer between compressor discs and air in compressor cavities under transient operating conditions. Calculation of transient heat fluxes from temperature measurements on compressor discs is a typical ill-posed inverse problem where small uncertainties of measurements can lead...
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... added compression will decrease the height of blades in high-pressure compressors and will require much smaller tip clearances to maintain high efficiency and reliability. Figure 1 shows the structure of a typical aero-engine high pressure compressor. The tip clearance is governed by the relative expansion of the casing and the rotor. ...
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... and fast predictive methods are important for engine clearance decisions using combined thermo-mechanical models across the full operating flight envelope. Under cruise conditions, the shroud is hotter than the throughflow (see Fig. 1 Physics of Fluids ARTICLE scitation.org/journal/phf and shroud. However, at other points in the flight cycle, the shroud can become colder than the cob, and this suppresses buoyancy effects; here, stratified flow may form with heat transfer governed by conduction rather than convection. This large reduction of heat transfer, which ...
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... University of Sussex. The transient behavior of temperature was discussed, but the heat fluxes were not calculated. Though research on transient heat transfer on compressor disks is limited, there are a broad range of experimental, theoretical, and computational studies on steady-state heat transfer in different compressor cavities. As shown in Fig. 1, there are axial gaps between adjacent disk cobs and these are referred to as open cavities. In some compressors, the axial gaps do not exist, leaving closed spaces between the shroud, the two adjacent disk and a hub. These configurations, often found in industrial compressors, are referred to as closed cavities. This section focuses ...
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... disks were gradually cooled to a virtually isothermal condition. Figure 10(c) shows the history of the non-dimensional parameters Re / ; bDT, and Gr and v: as the transient progressed, bDT decreased and Re / was kept constant, leading to a decrease in Gr and an increase in v. Figure 11 shows the transient temperature and the variation of non-dimensional parameters for the other three Re / (cases A, C, and D). The temperature distributions for case A (Re / ¼ 7 Â 10 5 ) were similar to those for case B. However, at Re / > 2:1 Â 10 6 (cases C and D), the disks were remained heated at the end of the transient. ...
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... disks were gradually cooled to a virtually isothermal condition. Figure 10(c) shows the history of the non-dimensional parameters Re / ; bDT, and Gr and v: as the transient progressed, bDT decreased and Re / was kept constant, leading to a decrease in Gr and an increase in v. Figure 11 shows the transient temperature and the variation of non-dimensional parameters for the other three Re / (cases A, C, and D). The temperature distributions for case A (Re / ¼ 7 Â 10 5 ) were similar to those for case B. However, at Re / > 2:1 Â 10 6 (cases C and D), the disks were remained heated at the end of the transient. ...
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... radial location x à where / ¼ 0 indicates the radius where the disk temperature is equal to the core temperature. Figure 12(a) shows that at Fo < 0:022; x à decreases as Fo increases, leading to a decrease in h x à (the disk temperature at x à ) and, hence, the core temperature. As Fo approaches 0.16, the heat flux gradually decreases to virtually zero, which implies that the flow becomes stratified. ...
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... Fo approaches 0.16, the heat flux gradually decreases to virtually zero, which implies that the flow becomes stratified. Figure 13(b) shows the radial distributions of the heat fluxes and their 95% confidence intervals at different Fo numbers for case B. At Fo ¼ 0, the steady-state disk heat flux reaches zero at x à ¼ 0:7, which is consistent with experiments in Ref. 4. At Fo ¼ 0.02, the radial location is close to x a , showing a dramatic decrease in the core temperature. Though the disk temperature at x b decreases dramatically, the disk heat flux / b at Fo ¼ 0.02 remains at a value of 4. This implies a constant temperature difference between the core and the disk at x ¼ x b , which suggests that the response speed of the core is similar to that of the outer part of the disk and much faster than that of the inner part. ...
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... fluxes are positive at all radii when Fo > 0:04, which suggests that the core temperature becomes lower than the temperature of the disk. Figure 13 also presents the calculated heat flux distributions for cases A, C, and D. The fluxes / b at Fo ¼ 0 stay almost constant from case A to case C and decrease at case D, owing to the increase in the compressibility parameter v 0 (see Table II). The calculated heat fluxes for cases A and C show similar behavior to that for case B: the flow gradually moves away from the buoyancy-induced regime and becomes stratified. ...
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... However, this configuration is not yet applicable. In addition, Tang and Cao et al. [25,26] used Bayesian modeling to tackle the inverse heat transfer problem on the disk. It should be noted that the radial pre-swirl system operates in a hightemperature environment, and thermal conditions significantly impact cooling performance. ...
Impellers are utilized to increase pressure to ensure that a radial pre-swirl system can provide sufficient cooling airflow to the turbine blades. In the open literature, the pressurization mechanism of the impellers was investigated. However, the effect of impellers on the cooling performance of the radial pre-swirl system was not clear. To solve the aforementioned problem, tests were carried out to assess the temperature drop in a radial pre-swirl system with various impeller configurations (impeller lengths l/b ranging from 0 to 0.333). Furthermore, numerical simulations were used to investigate the flow and heat transfer characteristics of the radial pre-swirl system at high rotating Reynolds numbers. Theoretical and experimental investigations revealed that the pre-swirl jet and output power generate a significant temperature drop, but the impellers have no obvious effect on the system temperature drop. By increasing the swirl ratio, the impellers reduce the field synergy angle and thus improve convective heat transfer on the turbine disk. In addition, increasing the impeller length can reduce the volume-averaged field synergy angle and improve heat transfer, but the improvement effectiveness decreases as the impeller length increases. Thus, the study concluded that impellers could improve the cooling performance of the radial pre-swirl system by enhancing disk cooling.
... Notably, Bohn et al. were pioneers in this field 19,20 , contributing significantly to the design and development of testing rigs to advance understanding in the domain. In response to these findings, considerable progress has been made in analytical modeling for sealed cavities, including the development of fast Bayesian models [21][22][23] and theoretical models for estimating heat transfer based on flat plate correlations 24,25 . These models reveal that the Nusselt number is strongly influenced by the radial distribution of disk temperature and compressibility effects 26,27 . ...
Turbofan compressor cooling circuits exhibit inherent unsteadiness within their cavities due to the interplay of forced and natural convection phenomena. This dynamic is fueled by axial cooling throughflow, centrifugal forces, and large temperature gradients. This paper introduces an extended compressible lattice-Boltzmann approach tailored for accurately modeling centrifugal buoyancy-driven flows in such cavities. The approach integrates a local rotating reference frame model into a hybrid thermal lattice Boltzmann method, facilitating the simulation of rotating flows of perfect gases. Moreover, a new mass-conserving boundary treatment, based on the reconstruction of distribution functions, enhances precision in predicting rotor disk heat transfer. Finally, an adapted direct-coupling mesh-refinement strategy, accounting for source terms at grid transitions, enables efficient high buoyancy flow simulations. The proposed approach effectively recovers flow and heat transfer mechanisms on sealed and open rotating compressor cavity rigs, spanning a large range of Rayleigh numbers (up to 109). Through an analysis of the compressibility effects, adjustments to the adiabatic exponent and Eckert number allow for a significant boost in computational speed without undermining the reliability of the flow and heat transfer dynamics, aligning well with established theoretical models and numerical studies. With computational efficiency that outperforms conventional compressible finite volume solvers, the proposed approach stands as a promising method for industrial-scale modeling of turbomachinery cooling circuits.
... Thus, predicting the temperature and heat flux on the disk aids engineers in their design process. Tang et al. [24] and Cao et al. [18] have developed models for predicting compressor and turbine disks in recent years. They first determine the temperature distribution on the disks using Bayesian models after obtaining the heat flux through experiments or computations. ...
... For Eqs (24) to (27) ...
In the secondary air system (SAS) of an aeroengine, co-rotating cavities with radial flow are in charge of extracting airflow from the compressor and providing it to the turbine. In high-speed cavities, pressure and temperature have a strong coupling correlation, which had not been investigated in previous studies. Accurate monitoring of airflow quality is a prerequisite for improving its cooling efficiency. In this study, theoretical analysis and verified numerical simulation were used to investigate the flow and heat transfer in the cavities, and a coupled prediction model (CPM) was developed to study the correlation among velocity, pressure and temperature. The results revealed that density, viscosity, and swirl ratio were important mediums for coupling pressure and temperature. Furthermore, autocorrelations existed in velocity, pressure, and temperature, and their fluctuations were rapidly transmitted through the mediums and eventually backfired. The CPM, which could be used to predict aerodynamic parameters, showed a relative average error of less than 10% compared to the Reynolds stress model (RSM).
We study the Bayesian inverse problem of inferring the Biot number, a spatio-temporal heat-flux parameter in a PDE model. This is an ill-posed problem where standard optimisation yields unphysical inferences. We introduce a training scheme that uses temperature data to adaptively train a neural-network surrogate to simulate the parametric forward model. This approach approximates forward and inverse solution together, by simultaneously identifying an approximate posterior distribution over the Biot number, and weighting the forward training loss according to this approximation. Utilising random Chebyshev series, we outline how to approximate an arbitrary Gaussian process prior, and using the surrogate we apply Hamiltonian Monte Carlo (HMC) to efficiently sample from the corresponding posterior distribution. We derive convergence of the surrogate posterior to the true posterior distribution in the Hellinger metric as our adaptive loss function approaches zero. Furthermore, we describe how this surrogate-accelerated HMC approach can be combined with a traditional PDE solver in a delayed-acceptance scheme to a-priori control the posterior accuracy, thus overcoming a major limitation of deep learning-based surrogate approaches, which do not achieve guaranteed accuracy a-priori due to their non-convex training. Biot number calculations are involved turbo-machinery design, which is safety critical and highly regulated, therefore it is important that our results have such mathematical guarantees. Our approach achieves fast mixing in high-dimensional parameter spaces, whilst retaining the convergence guarantees of a traditional PDE solver, and without the burden of evaluating this solver for proposals that are likely to be rejected. Numerical results compare the accuracy and efficiency of the adaptive and general training regimes, as well as various Markov chain Monte Carlo proposals strategies.
