Heat transfer from an air-cooled rotating disk

1974 ◽  
Vol 336 (1607) ◽  
pp. 453-473 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Rotating Disk ◽  
Experimental Results ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Wide Range ◽  
The Mean ◽  
Radial Outflow

This paper describes a combined theoretical and experimental investigation into the heat transfer from a disk rotating close to a stator with a radial outflow of coolant. Experimental results are obtained from a 762 mm diameter disk, rotating up to 4000 rev/min at axial clearances from 2 to 230 mm from a stator of the same diameter, with coolant flow rates up to 0.7 kg/s. Mean Nusselt numbers are presented for the free disk, the disk rotating close to an unshrouded stator with no coolant outflow, the disk rotating close to a shrouded and unshrouded stator with coolant outflow, and for the unshrouded stator itself. Numerical solutions of the turbulent boundary layer equations are in satisfactory agreement with the experimentally determined mean Nusselt numbers for the air-cooled disk over a wide range of conditions. At large ratios of mass flow rate/rotational speed the mean Nusselt numbers for the air-cooled disk are independent of rotation, and both the numerical solutions and experimental results become asymptotic to an approximate solution of the boundary layer equations.

Heat Transfer From a Shrouded Disk System With a Radial Outflow of Coolant

1975 ◽  
Vol 97 (1) ◽  
pp. 28-35 ◽  
Author(s):  
C. M. Haynes ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Disk System ◽  
Flow Rates ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
The Mean ◽  
Radial Outflow ◽  
Plane Disk ◽  
System Geometry

This paper describes a combined theoretical and experimental study of the heat transfer from an air-cooled gas turbine disk using the model of a plane disk rotating close to a shrouded stator. Numerical solutions of the boundary layer equations are obtained by assuming a modified system geometry, and it is shown that this technique yields adequate estimates of moment coefficients and mean Nusselt numbers for the air-cooled disk. Experimental results show the effect of rotational speeds up to 4000 rev/min, coolant flow rates up to 2 lb/s, stator clearances and shroud clearances up to 2.7 in., on the mean Nusselt numbers for a 30-in-dia disk and its stator.

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.

Prediction of Heat Transfer in a Rotating Cavity With a Radial Outflow

1991 ◽  
Vol 113 (1) ◽  
pp. 115-122 ◽  
Author(s):  
C. L. Ong ◽  
J. M. Owen
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Eddy Viscosity Model ◽  
Rotating Cavity ◽  
Wide Range ◽  
Turbine Disks ◽  
Radial Outflow ◽  
Cooling Air

Solutions of the differential boundary-layer equations, using the Keller-box scheme and the Cebeci-Smith eddy-viscosity model for turbulent flow, have been used to predict the Nusselt numbers on the disks of a heated rotating cavity with a radial outflow of cooling air. Computed Nusselt numbers were in satisfactory agreement with analytical solutions of the elliptic equations for laminar flow and with solutions of the integral equations for turbulent flow. For a wide range of flow rates, rotational speeds, and disk-temperature profiles, the computed Nusselt numbers were in mainly good agreement with measurements obtained from an air-cooled rotating cavity. It is concluded that the boundary-layer equations should provide solutions accurate enough for application to air-cooled gas turbine disks.

Prediction of Heat Transfer in a Rotating Cavity With a Radial Outflow

1989 ◽  
Author(s):  
C. L. Ong ◽  
J. M. Owen
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Eddy Viscosity Model ◽  
Box Scheme ◽  
Rotating Cavity ◽  
Wide Range ◽  
Radial Outflow ◽  
Cooling Air

Solutions of the differential boundary-layer equations, using the Keller-box scheme and the Cebeci-Smith eddy-viscosity model for turbulent flow, have been used to predict the Nusselt numbers on the discs of a heated rotating cavity with a radial outflow of cooling air. Computed Nusselt numbers were in satisfactory agreement with analytical solutions of the elliptic equations for laminar flow and with solutions of the integral equations for turbulent flow. For a wide range of flow rates, rotational speeds and disc-temperature profiles, the computed Nusselt numbers were in mainly good agreement with measurements obtained from an air-cooled rotating cavity. It is concluded that the boundary-layer equations should provide solutions accurate enough for application to air-cooled gas-turbine discs.

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.

The effect of convective heat transfer on unsteady boundary-layer separation

2001 ◽  
Vol 428 ◽  
pp. 107-131 ◽  
Author(s):  
K. W. CASSEL
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Inclination Angle ◽  
Numerical Solutions ◽  
Heated Surface ◽  
Boundary Layer Separation ◽  
Convection Boundary Layer ◽  
Grashof Number ◽  
Boundary Layer Equations ◽  
Unsteady Mixed Convection

The unsteady evolution of a boundary layer induced by a rectilinear vortex convecting above a heated surface is considered numerically. This model problem is representative of the types of interactions that can occur when vortices encounter solid surfaces in a wide variety of diverse applications involving high-Reynolds-number and high-Grashof-number flows. It is known that in the case without heat transfer, the vortex-induced boundary layer evolves toward a singularity as it forms a sharp spike that erupts away from the surface. Numerical solutions of the unsteady mixed-convection boundary-layer equations in the Boussinesq limit are obtained in Lagrangian coordinates. Solutions for various values of the inclination angle of the surface and Grashof number show that the coupling between the fluid flow and heat transfer can have a dramatic effect upon the transport of momentum and energy within the boundary layer induced by the vortex. The unsteady eruption convects high-temperature, near-wall fluid away from the surface and causes large gradients in the thermal boundary layer. The buoyancy force acting on the heated boundary-layer fluid can also have a significant impact on the unsteady separation process, either accelerating or delaying it, depending upon the inclination angle of the surface.

Nonsimilar Boundary-Layer Heat Transfer of a Rotating Cone in Forced Flow

1967 ◽  
Vol 89 (2) ◽  
pp. 139-145 ◽  
Author(s):  
J. C. Y. Koh ◽  
J. F. Price
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Cone Angle ◽  
Rotating Disk ◽  
Forced Flow ◽  
Degenerate Problem ◽  
Prandtl Numbers ◽  
Half Cone ◽  
Half Cone Angle

The nonsimilar boundary-layer flow and heat transfer of a cone rotating in a forced-flow field are investigated. Numerical solutions are shown for a half-cone angle of 53.5 deg with parameters (vw/ue)2 ranging from 0 to 20, and with Prandtl numbers from 0.2 to 10. With a half-cone angle of 90 deg (so that one has a rotating disk), the degenerate problem is solved in the same manner.

A singularity in thermal boundary-layer flow on a horizontal surface

1992 ◽  
Vol 242 ◽  
pp. 419-440 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Rational Numbers ◽  
Velocity Fields ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Buoyancy Flows ◽  
Temperature And Velocity Fields

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity

1972 ◽  
Vol 51 (1) ◽  
pp. 137-157 ◽  
Author(s):  
R. C. Ackerberg ◽  
J. H. Phillips
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Stream Velocity ◽  
Main Stream ◽  
Mean Flow ◽  
Boundary Layer Equations ◽  
Damped Oscillations ◽  
Asymptotic Values ◽  
The Mean

Asymptotic and numerical solutions of the unsteady boundary-layer equations are obtained for a main stream velocity given by equation (1.1). Far downstream the flow develops into a double boundary layer. The inside layer is a Stokes shear-wave motion, which oscillates with zero mean flow, while the outer layer is a modified Blasius motion, which convects the mean flow downstream. The numerical results indicate that most flow quantities approach their asymptotic values far downstream through damped oscillations. This behaviour is attributed to exponentially small oscillatory eigenfunctions, which account for different initial conditions upstream.

Sign in / Sign up

Export Citation Format

Share Document