Computation of Heat Transfer in Rotating Cavities Using a Two-Equation Model of Turbulence

1990 ◽  
Author(s):  
A. P. Morse ◽  
C. L. Ong
Keyword(s):  
Heat Transfer ◽  
Turbulence Model ◽  
Radial Direction ◽  
Reynolds Numbers ◽  
Systematic Errors ◽  
Equation Model ◽  
Sufficient Accuracy ◽  
Nusselt Numbers ◽  
Radial Outflow ◽  
Cooling Air

The paper presents finite-difference predictions for the convective heat transfer in symmetrically-heated rotating cavities subjected to a radial outflow of cooling air. An elliptic calculation procedure has been used, with the turbulent fluxes estimated by means of a low Reynolds number k-ε model and the familiar ‘turbulence Prandtl number’ concept. The predictions extend to rotational Reynolds numbers of 3.7 × 106 and encompass cases where the disc temperatures may be increasing, constant or decreasing in the radial direction. It is found that the turbulence model leads to predictions of the local and average Nusselt numbers for both discs which are generally within ± 10% of the values from published experimental data, although there appear to be larger systematic errors for the upstream disc than for the downstream disc. It is concluded that the calculations are of sufficient accuracy for engineering design purposes, but that improvements could be brought about by further optimization of the turbulence model.

Computation of Heat Transfer in Rotating Cavities Using a Two-Equation Model of Turbulence

1992 ◽  
Vol 114 (1) ◽  
pp. 247-255 ◽  
Author(s):  
A. P. Morse ◽  
C. L. Ong
Keyword(s):  
Heat Transfer ◽  
Turbulence Model ◽  
Radial Direction ◽  
Reynolds Numbers ◽  
Systematic Errors ◽  
Equation Model ◽  
Sufficient Accuracy ◽  
Nusselt Numbers ◽  
Radial Outflow ◽  
Cooling Air

The paper presents finite-difference predictions for the convective heat transfer in symmetrically heated rotating cavities subjected to a radial outflow of cooling air. An elliptic calculation procedure has been used, with the turbulent fluxes estimated by means of a low Reynolds number k–ε model and the familiar “turbulence Prandtl number” concept. The predictions extend to rotational Reynolds numbers of 3.7 × 106 and encompass cases where the disk temperatures may be increasing, constant, or decreasing in the radial direction. It is found that the turbulence model leads to predictions of the local and average Nusselt numbers for both disks that are generally within ± 10 percent of the values from published experimental data, although there appear to be larger systematic errors for the upstream disk than for the downstream disk. It is concluded that the calculations are of sufficient accuracy for engineering design purposes, but that improvements could be brought about by further optimization of the turbulence model.

scholarly journals Heat Transfer in an Air-Cooled Rotor-Stator System

1994 ◽  
Author(s):  
Jian-Xin Chen ◽  
Xiaopeng Gan ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Turbulence Model ◽  
Computational Study ◽  
Reynolds Numbers ◽  
Flow Rates ◽  
Nusselt Numbers ◽  
Heated Disc ◽  
Radial Outflow ◽  
Cooling Air

This paper describes a combined experimental and computational study of the heat transfer from an electrically-heated disc rotating close to an unheated stator. A radial outflow of cooling air was used to remove heat from the disc, and local Nusselt numbers were measured, using fluxmeters at seven radial locations, for nondimensional flow rates up to C = 9680 and rotational Reynolds numbers up to Reφ = 1.2 × 106. Computations were carried out using an elliptic solver with a low-Reynolds-number k-ε turbulence model, and the agreement between the measured and computed velocities and Nusselt numbers was mainly good.

Heat Transfer in an Air-Cooled Rotor–Stator System

1996 ◽  
Vol 118 (3) ◽  
pp. 444-451 ◽  
Author(s):  
J.-X. Chen ◽  
X. Gan ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Turbulence Model ◽  
Computational Study ◽  
Reynolds Numbers ◽  
Flow Rates ◽  
Nusselt Numbers ◽  
Heated Disk ◽  
Radial Outflow ◽  
Cooling Air

This paper describes a combined experimental and computational study of the heat transfer from an electrically heated disk rotating close to an unheated stator. A radial outflow of cooling air was used to remove heat from the disk, and local Nusselt numbers were measured, using fluxmeters at seven radial locations, for nondimensional flow rates up to Cw = 9680 and rotational Reynolds numbers up to Reφ = 1.2 × 106 Computations were carried out using an elliptic solver with a low-Reynolds-number k–ε turbulence model, and the agreement between the measured and computed velocities and Nusselt numbers was mainly good.

Heat Transfer in a “Cover-Plate” Preswirl Rotating-Disk System

1999 ◽  
Vol 121 (2) ◽  
pp. 249-256 ◽  
Author(s):  
R. Pilbrow ◽  
H. Karabay ◽  
M. Wilson ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Turbine Disk ◽  
Cover Plate ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Cooling Air ◽  
Plate System

In most gas turbines, blade-cooling air is supplied from stationary preswirl nozzles that swirl the air in the direction of rotation of the turbine disk. In the “cover-plate” system, the preswirl nozzles are located radially inward of the blade-cooling holes in the disk, and the swirling airflows radially outward in the cavity between the disk and a cover-plate attached to it. In this combined computational and experimental paper, an axisymmetric elliptic solver, incorporating the Launder–Sharma and the Morse low-Reynolds-number k–ε turbulence models, is used to compute the flow and heat transfer. The computed Nusselt numbers for the heated “turbine disk” are compared with measured values obtained from a rotating-disk rig. Comparisons are presented, for a wide range of coolant flow rates, for rotational Reynolds numbers in the range 0.5 X 106 to 1.5 X 106, and for 0.9 < βp < 3.1, where βp is the preswirl ratio (or ratio of the tangential component of velocity of the cooling air at inlet to the system to that of the disk). Agreement between the computed and measured Nusselt numbers is reasonably good, particularly at the larger Reynolds numbers. A simplified numerical simulation is also conducted to show the effect of the swirl ratio and the other flow parameters on the flow and heat transfer in the cover-plate system.

Heat Transfer in a “Cover-Plate” Pre-Swirl Rotating-Disc System

1998 ◽  
Author(s):  
Robert Pilbrow ◽  
Hasan Karabay ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Numbers ◽  
Cover Plate ◽  
Swirl Ratio ◽  
Rotating Disc ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Turbine Disc ◽  
Cooling Air

In most gas turbines, blade-cooling air is supplied from stationary pre-swirl nozzles that swirl the air in the direction of rotation of the turbine disc. In the “cover-plate” system, the pre-swirl nozzles are located radially inward of the blade-cooling holes in the disc, and the swirling air flows radially outwards in the cavity between the disc and a cover-plate attached to it. In this combined computational and experimental paper, an axisymmetric elliptic solver, incorporating the Launder-Sharma and the Morse low-Reynolds-number k-ε turbulence models, is used to compute the flow and heat transfer. The computed Nusselt numbers for the heated “turbine disc” are compared with measured values obtained from a rotating-disc rig. Comparisons are presented, for a wide range of coolant flow rates, for rotational Reynolds numbers in the range 0.5 × 106 to 1.5 × 106, and for 0.9 < βp < 3.1, where βp is the pre-swirl ratio (or ratio of the tangential component of velocity of the cooling air at inlet to the system to that of the disc). Agreement between the computed and measured Nusselt numbers is reasonably good, particularly at the larger Reynolds numbers. A simplified numerical simulation is also conducted to show the effect of the swirl ratio and the other flow parameters on the flow and heat transfer in the cover-plate system.

Heat Transfer From Air-Cooled Contrarotating Disks

1997 ◽  
Vol 119 (1) ◽  
pp. 61-67 ◽  
Author(s):  
J.-X. Chen ◽  
X. Gan ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Rate ◽  
Reynolds Numbers ◽  
The Other ◽  
Reynolds Analogy ◽  
Flow Rates ◽  
Nusselt Numbers ◽  
Radial Outflow ◽  
Equivalent Conditions

A superposed radial outflow of air is used to cool two disks that are rotating at equal and opposite speeds at rotational Reynolds numbers up to 1.2 × 106. One disk, which is heated up to 100°C, is instrumented with thermocouples and fluxmeters; the other disk, which is unheated, is made from transparent polycarbonate to allow the measurement of velocity using an LDA system. Measured Nusselt numbers and velocities are compared with computations made using an axisymmetric elliptic solver with a low-Reynolds-number k–ε turbulence model. Over the range of flow rates and rotational speeds tested, agreement between the computations and measurements is mainly good. As suggested by the Reynolds analogy, the Nusselt numbers for contrarotating disks increase strongly with rotational speed and weakly with flow rate; they are lower than the values obtained under equivalent conditions in a rotor–stator system.

The Effect of Disk Geometry on Heat Transfer in a Rotating Cavity With a Radial Outflow of Fluid

1988 ◽  
Vol 110 (1) ◽  
pp. 70-77 ◽  
Author(s):  
P. R. Farthing ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Flow Visualization ◽  
Source Region ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Via Holes ◽  
Turbine Disks ◽  
Radial Outflow ◽  
Cooling Air

Flow visualization and heat transfer measurements have been made in a cavity comprising two nonplane disks of 762 mm diameter and a peripheral shroud, all of which could be rotated up to 2000 rpm. “Cobs,” made from a lightweight foam material and shaped to model the geometry of turbine disks, were attached to the center of each disk. Cooling air at flow rates up to 0.1 kg/s entered the cavity through the center of the “upstream” disk and left via holes in the shroud. The flow structure was found to be similar to that observed in earlier tests for the plane-disk case: a source region, Ekman layers, sink layer, and interior core were observed by flow visualization. Providing the source region did not fill the entire cavity, solutions of the turbulent integral boundary-layer equations provided a reasonable approximation to the Nusselt numbers measured on the heated “downstream” disk.

scholarly journals Flow in a Rotating Cavity With a Peripheral Inlet and Outlet of Cooling Air

1996 ◽  
Author(s):  
Xiaopeng Gan ◽  
Iraj Mirzaee ◽  
J. Michael Owen ◽  
D. Andrew S. Rees ◽  
Michael Wilson
Keyword(s):  
Boundary Layers ◽  
Turbulence Model ◽  
Laser Doppler Anemometry ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Recirculation Region ◽  
Rotating Disc ◽  
The Core ◽  
Radial Outflow ◽  
Cooling Air

In some engines, corotating gas–turbine discs are cooled by air introduced at the periphery of the system. The air enters through holes in a stationary peripheral casing and leaves through the rim seals between the casing and the discs. This paper describes a combined computational and experimental study of such a system for a range of flowrates and for rotational Reynolds numbers of up to Reϕ = 1.5 × 106. Computations are made using an axisymmetric elliptic solver, incorporating the Launder–Sharma low–Reynolds–number k–ε turbulence model, and velocity measurements are obtained using laser–Doppler anemometry. The stationary peripheral casing creates a recirculation region: there is radial outflow in boundary layers on the discs and inflow in the core between the boundary layers. The radial extent of the recirculation region increases as the flow rate increases and as the rotational speed decreases. In the core, the radial and tangential components of velocity, Vr and Vϕ, are invariant in the axial direction, and the measured values of Vϕ conform to a Rankine–vortex flow. The agreement between the computed and measured velocities is not as good as that found for other rotating–disc systems, and deficiencies in the turbulence model are believed to be responsible.

scholarly journals Convective Heat Transfer in a Rotating Cylindrical Cavity

1982 ◽  
Author(s):  
J. M. Owen ◽  
H. S. Onur
Keyword(s):  
Heat Transfer ◽  
Flow Visualization ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Nusselt Numbers ◽  
Gap Ratio ◽  
Wide Range ◽  
The Mean ◽  
Radial Outflow ◽  
Good Agreement

In order to gain an understanding of the conditions inside air-cooled gas-turbine rotors, flow visualization, laser-doppler anemometry and heat-transfer measurements have been made in a rotating cavity with either an axial throughflow or a radial outflow of coolant. For the axial throughflow tests, a correlation has been obtained for the mean Nusselt number in terms of the cavity gap ratio, the axial Reynolds number and rotational Grashof number. For the radial outflow tests, velocity measurements are in good agreement with solutions of the linear (laminar and turbulent) Ekman layer equations, and flow visualization has revealed the destabilizing effect of buoyancy forces on the flow structure. The mean Nusselt numbers have been correlated, for the radial outflow case, over a wide range of gap ratios, coolant flow rates, rotational Reynolds numbers and Grashof numbers. As well as the three (forced convection) regimes established from previous experiments, a fourth (free convection) regime has been identified.

Convective Heat Transfer in a Rotating Cylindrical Cavity

1983 ◽  
Vol 105 (2) ◽  
pp. 265-271 ◽  
Author(s):  
J. M. Owen ◽  
H. S. Onur
Keyword(s):  
Heat Transfer ◽  
Flow Visualization ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Nusselt Numbers ◽  
Gap Ratio ◽  
Wide Range ◽  
The Mean ◽  
Radial Outflow ◽  
Good Agreement

In order to gain an understanding of the conditions inside air-cooled, gas-turbine rotors, flow visualization, laser-doppler anemometry, and heat-transfer measurements have been made in a rotating cavity with either an axial throughflow or a radial outflow of coolant. For the axial throughflow tests, a correlation has been obtained for the mean Nusselt number in terms of the cavity gap ratio, the axial Reynolds number, and rotational Grashof number. For the radial outflow tests, velocity measurements are in good agreement with solutions of the linear (laminar and turbulent) Ekman layer equations, and flow visualization has revealed the destabilizing effect of buoyancy forces on the flow structure. The mean Nusselt numbers have been correlated, for the radial outflow case, over a wide range of gap ratios, coolant flow rates, rotational Reynolds numbers, and Grashof numbers. As well as the three (forced convection) regimes established from previous experiments, a fourth (free convection) regime has been identified.

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