Theoretical Model of Buoyancy-Induced Heat Transfer in Closed Compressor Rotors

2017 ◽  
Author(s):  
Hui Tang ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Gravitational Acceleration ◽  
Centripetal Acceleration ◽  
Closed Cavity ◽  
Nusselt Numbers ◽  
Industrial Gas Turbines ◽  
Induced Flow ◽  
Cooling Air ◽  
Buoyancy Induced Flow

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.

Theoretical Model of Buoyancy-Induced Heat Transfer in Closed Compressor Rotors

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Hui Tang ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Gravitational Acceleration ◽  
Centripetal Acceleration ◽  
Closed Cavity ◽  
Nusselt Numbers ◽  
Industrial Gas Turbines ◽  
Induced Flow ◽  
Aero Engines ◽  
Buoyancy Induced Flow

The cavities between the rotating compressor disks in aero-engines are open, and there is an axial throughflow of cooling air in the annular space between the center of the disks 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 center of the compressor disks—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 center of compressor disks—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.

Measurement of Heat Transfer and Flow Structures in a Closed Rotating Cavity

2022 ◽  
Author(s):  
Richard Jackson ◽  
Hui Tang ◽  
James Scobie ◽  
J. Michael Owen ◽  
Gary Lock
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Pressure Sensors ◽  
Flow Structures ◽  
Closed Cavity ◽  
Experimental Range ◽  
Wide Range ◽  
Industrial Gas Turbines ◽  
Induced Flow ◽  
Compressibility Effects

Abstract 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.

Measurement of Heat Transfer and Flow Structures in a Closed Rotating Cavity

2021 ◽  
Author(s):  
Richard W. Jackson ◽  
Hui Tang ◽  
James A. Scobie ◽  
J. Michael Owen ◽  
Gary D. Lock
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Pressure Sensors ◽  
Flow Structures ◽  
Closed Cavity ◽  
Experimental Range ◽  
Wide Range ◽  
Industrial Gas Turbines ◽  
Induced Flow ◽  
Compressibility Effects

Abstract 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.

Measurement and Analysis of Buoyancy-Induced Heat Transfer in Aero-Engine Compressor Rotors

2020 ◽  
Author(s):  
Richard W. Jackson ◽  
Dario Luberti ◽  
Hui Tang ◽  
Oliver J. Pountney ◽  
James A. Scobie ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Outer Region ◽  
Conjugate Problem ◽  
Radial Temperature ◽  
Nusselt Numbers ◽  
Induced Flow ◽  
Aero Engines ◽  
Inner Region ◽  
Buoyancy Induced Flow

Abstract The flow inside cavities between co-rotating compressor discs of aero-engines is driven by buoyancy, with Grashof numbers exceeding 1013. This phenomenon creates a conjugate problem: the Nusselt numbers depend on the radial temperature distribution of the discs, and the disc temperatures depend on the Nusselt numbers. Furthermore, Coriolis forces in the rotating fluid generate cyclonic and anti-cyclonic circulations inside the cavity. Such flows are three-dimensional, unsteady and unstable, and it is a challenge to compute and measure the heat transfer from the discs to the axial throughflow in the compressor. In this paper, Nusselt numbers are experimentally determined from measurements of steady-state temperatures on the surfaces of both discs in a rotating cavity of the Bath Compressor-Cavity Rig. The data are collected over a range of engine-representative parameters and are the first results from a new experimental facility specifically designed to investigate buoyancy-induced flow. The radial distributions of disc temperature were collected under carefully-controlled thermal boundary conditions appropriate for analysis using a Bayesian model combined with the equations for a circular fin. The Owen-Tang buoyancy model has been used to compare predicted radial distributions of disc temperatures and Nusselt numbers with some of the experimentally determined values, taking account of radiation between the interior surfaces of the cavity. The experiments show that the average Nusselt numbers on the disc increase as the buoyancy forces increase. At high rotational speeds the temperature rise in the core, created by compressibility effects in the air, attenuates the heat transfer and there is a critical rotational Reynolds number for which the Nusselt number is a maximum. In the cavity, there is an inner region dominated by forced convection and an outer region dominated by buoyancy-induced flow. The inner region is a mixing region, in which entrained cold throughflow encounters hot flow from the Ekman layers on the discs. Consequently, the Nusselt numbers on the downstream disc in the inner region tend to be higher than those on the upstream disc.

Flow and Heat Transfer in a Preswirl Rotor–Stator System

1997 ◽  
Vol 119 (2) ◽  
pp. 364-373 ◽  
Author(s):  
M. Wilson ◽  
R. Pilbrow ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Heat Fluxes ◽  
Valuable Insight ◽  
Swirl Ratio ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Air Temperatures ◽  
Via Holes ◽  
Cooling Air

Conditions in the internal-air system of a high-pressure turbine stage are modeled using a rig comprising an outer preswirl chamber separated by a seal from an inner rotor-stator system. Preswirl nozzles in the stator supply the “blade-cooling” air, which leaves the system via holes in the rotor, and disk-cooling air enters at the center of the system and leaves through clearances in the peripheral seals. The experimental rig is instrumented with thermocouples, fluxmeters, pitot tubes, and pressure taps, enabling temperatures, heat fluxes, velocities, and pressures to be measured at a number of radial locations. For rotational Reynolds numbers of Reφ ≃ 1.2 × 106, the swirl ratio and the ratios of disk-cooling and blade-cooling flow rates are chosen to be representative of those found inside gas turbines. Measured radial distributions of velocity, temperature, and Nusselt number are compared with computations obtained from an axisymmetric elliptic solver, featuring a low-Reynolds-number k–ε turbulence model. For the inner rotor-stator system, the computed core temperatures and velocities are in good agreement with measured values, but the Nusselt numbers are underpredicted. For the outer preswirl chamber, it was possible to make comparisons between the measured and computed values for cooling-air temperatures but not for the Nusselt numbers. As expected, the temperature of the blade-cooling air decreases as the inlet swirl ratio increases, but the computed air temperatures are significantly lower than the measured ones. Overall, the results give valuable insight into some of the heat transfer characteristics of this complex system.

scholarly journals Buoyancy-Induced Flow and Heat Transfer in Compressor Rotors

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Hui Tang ◽  
Mark R. Puttock-Brown ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Temperature Rise ◽  
Radial Growth ◽  
Radial Clearance ◽  
Rotating Disks ◽  
Compressor Blades ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Induced Flow ◽  
Buoyancy Induced Flow

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.

scholarly journals Extension of Gas Turbine Disc Life by Retrofitting a Supplemental Cooling System

1985 ◽  
Author(s):  
D. Little ◽  
J. Wilson ◽  
J. Liburdi
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Cooling System ◽  
High Temperature Creep ◽  
Test Results ◽  
Drive Unit ◽  
Turbine Disc ◽  
Engineering Work ◽  
Industrial Gas Turbines ◽  
Cooling Air

The turbine disc lives in some industrial gas turbines are limited to much less than 100,000 hours by the formation of high temperature creep cracks when the engine is operated continuously at full load. Turbine users have experienced many costly repairs and even a wreck due to this recurring problem. The problem can be eliminated and the existing uncracked disc lives extended well beyond the 100,000 hour milestone by the retrofit of a supplemental disc cooling system. The engineering work involved in properly identifying the cause and designing the cooling modification, including performance, aerodynamic, cooling network, finite element heat transfer, and stress analysis is explained. The build and test of the prototype cooling air system on a mechanical drive unit is discussed and test results demonstrating the success of the method given. The concept of adding a supplemental disc cooling system to extend the expiring turbine disc lives of many mature frames has been demonstrated to be both practical and economical.

Use of Fin Equation to Calculate Nusselt Numbers for Rotating Discs

2015 ◽  
Author(s):  
Hui Tang ◽  
Tony Shardlow ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Conjugate Problem ◽  
Temperature Measurements ◽  
Rotating Disc ◽  
Nusselt Numbers ◽  
Rotating Discs ◽  
Induced Flow ◽  
Buoyancy Induced Flow

Conduction in thin discs can be modelled using the fin equation, and there are analytical solutions of this equation for a circular disc with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disc systems is a conjugate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number, Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disc temperature is known then Bi can be determined numerically. But the determination of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this paper, Bayesian statistics are applied to the inverse solution of the circular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy temperature measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating compressor discs.

scholarly journals Flow and Heat Transfer in a Pre-Swirl Rotor-Stator System

1995 ◽  
Author(s):  
Michael Wilson ◽  
Robert Pilbrow ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Heat Fluxes ◽  
Valuable Insight ◽  
Swirl Ratio ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Swirl Chamber ◽  
Air Temperatures ◽  
Cooling Air

Conditions in the internal-air system of a high-pressure turbine stage are modelled using a rig comprising an outer pre-swirl chamber separated by a seal from an inner rotor-stator system. Pre-swirl nozzles in the stator supply the “blade-cooling” air, which leaves the system via holes in the rotor, and disc-cooling air enters at the centre of the system and leaves through clearances in the peripheral seals. The experimental rig is instrumented with thermocouples, fluxmeters, pitot tubes and pressure taps enabling temperatures, heat fluxes, velocities and pressures to be measured at a number of radial locations. For rotational Reynolds numbers of Reϕ ≃ 1.2 × 106, the swirl ratio and the ratios of disc-cooling and blade-cooling flow rates are chosen to be representative of those found inside gas turbines. Measured radial distributions of velocity, temperature and Nusselt number are compared with computations obtained from an axisymmetric elliptic solver, featuring a low-Reynolds-number k-ε turbulence model. For the inner rotor-stator system, the computed core temperatures and velocities are in good agreement with measured values, but the Nusselt numbers are underpredicted. For the outer pre-swirl chamber, it was possible to make comparisons between the measured and computed values for cooling-air temperatures but not for the Nusselt numbers. As expected, the temperature of the blade-cooling air decreases as the swirl ratio increases, but the computed air temperatures are significantly lower than the measured ones. Overall, the results give valuable insight into some of the heat transfer characteristics of this complex system.

Buoyancy-Induced Flow in a Heated Rotating Cavity

2004 ◽  
Author(s):  
J. Michael Owen ◽  
Jonathan Powell
Keyword(s):  
Reynolds Numbers ◽  
Velocity Measurements ◽  
Turbine Engine ◽  
Nusselt Numbers ◽  
Rotating Cavity ◽  
Heated Disc ◽  
Flux Measurements ◽  
Induced Flow ◽  
Cooling Air ◽  
Buoyancy Induced Flow

Experimental measurements were made in a rotating-cavity rig with an axial throughflow of cooling air at the centre of the cavity, simulating the conditions that occur between corotating compressor discs of a gas-turbine engine. One of the discs in the rig was heated, and the other rotating surfaces were quasi-adiabatic; the temperature difference, between the heated disc and the cooling air was between 40 and 100 °C. Tests were conducted for axial Reynolds numbers, Rez, of the cooling air between 1.4 × 103 and 5 × 104, and for rotational Reynolds numbers, Reφ, between 4 × 105 and 3.2 × 106. Velocity measurements inside the rotating cavity were made using LDA, and temperatures and heat flux measurements on the heated disc were made using thermocouples and fluxmeters. The velocity measurements were consistent with a 3D, unsteady, buoyancy-induced flow in which there was a multicell structure comprising one, two or three pairs of cyclonic and anti-cyclonic vortices. The core of fluid between the boundary layers on the discs rotated at a slower speed than the discs, as found by other experimenters. At the smaller values of Rez, the radial distribution and magnitude of the local Nusselt numbers, Nu, were consistent with buoyancy-induced flow. At the larger values of Rez, the distribution of Nu changed, and its magnitude increased, suggesting the dominance of the axial throughflow.

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