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.

Boundary-Layer Flows in Rotating Cavities

1989 ◽  
Vol 111 (3) ◽  
pp. 341-348 ◽  
Author(s):  
C. L. Ong ◽  
J. M. Owen
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Reverse Flow ◽  
Source Region ◽  
Linear Equations ◽  
Inviscid Fluid ◽  
Eddy Viscosity Model ◽  
Wide Range ◽  
Radial Outflow

A rotating cylindrical cavity with a radial outflow of fluid provides a simple model of the flow between two corotating air-cooled gas-turbine disks. The flow structure comprises a source region near the axis of rotation, boundary layers on each disk, a sink layer on the peripheral shroud, and an interior core of rotating inviscid fluid between the boundary layers. In the source region, the boundary layers entrain fluid; outside this region, nonentraining Ekman-type layers are formed on the disks. In this paper, the differential boundary-layer equations are solved to predict the velocity distribution inside the entraining and nonentraining boundary layers and in the inviscid core. The equations are discretized using the Keller-box scheme, and the Cebeci–Smith eddy-viscosity model is used for the turbulent-flow case. Special problems associated with reverse flow in the nonentraining Ekman-type layers are successfully overcome. Solutions are obtained, for both laminar and turbulent flow, for the “linear equations” (where nonlinear inertial terms are neglected) and for the full nonlinear equations. These solutions are compared with earlier LDA measurements of the radial and tangential components of velocity made inside a rotating cavity with a radial outflow of air. Good agreement between the computations and the experimental data is achieved for a wide range of flow rates and rotational speeds.

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 in a Rotating Cavity With a Stationary Stepped Casing

1999 ◽  
Vol 121 (2) ◽  
pp. 281-287 ◽  
Author(s):  
I. Mirzaee ◽  
P. Quinn ◽  
M. Wilson ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Parameter ◽  
Rotating Disk ◽  
Nusselt Numbers ◽  
Rotating Cavity ◽  
Wide Range ◽  
Heated Disc ◽  
Turbine Disks ◽  
Cooling Air

In the system considered here, corotating “turbine” disks are cooled by air supplied at the periphery of the system. The system comprises two corotating disks, connected by a rotating cylindrical hub and shrouded by a stepped, stationary cylindrical outer casing. Cooling air enters the system through holes in the periphery of one disk, and leaves through the clearances between the outer casing and the disks. The paper describes a combined computational and experimental study of the heat transfer in the above-described system. In the experiments, one rotating disk is heated, the hub and outer casing are insulated, and the other disk is quasi-adiabatic. Thermocouples and fluxmeters attached to the heated disc enable the Nusselt numbers, Nu, to be determined for a wide range of rotational speeds and coolant flow rates. Computations are carried out using an axisymmetric elliptic solver incorporating the Launder–Sharma low-Reynolds-number k–ε turbulence model. The flow structure is shown to be complex and depends strongly on the so-called turbulent flow parameter, λT, which incorporates both rotational speed and flow rate. For a given value λT, the computations show that Nu increases as Reφ, the rotational Reynolds number, increases. Despite the complexity of the flow, the agreement between the computed and measured Nusselt numbers is reasonably good.

Rotating Cavity With Axial Throughflow of Cooling Air: Heat Transfer

1992 ◽  
Vol 114 (1) ◽  
pp. 229-236 ◽  
Author(s):  
P. R. Farthing ◽  
C. A. Long ◽  
J. M. Owen ◽  
J. R. Pincombe
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Simple Correlation ◽  
Nusselt Numbers ◽  
Rotating Cavity ◽  
Wide Range ◽  
Effects Of Radiation ◽  
Increasing Temperature ◽  
Cooling Air ◽  
Made In

Heat transfer measurements were made in two rotating cavity rigs, in which cooling air passed axially through the center of the disks, for a wide range of flow rates, rotational speeds, and temperature distributions. For the case of a symmetrically heated cavity (in which both disks have the same temperature distribution), it was found that the distributions of local Nusselt numbers were similar for both disks and the effects of radiation were negligible. For an asymmetrically heated cavity (in which one disk is hotter than the other), the Nusselt numbers on the hotter disk were similar to those in the symmetrically heated cavity but greater in magnitude than those on the colder disks; for this case, radiation from the hot to the cold disk was the same magnitude as the convective heat transfer. Although the two rigs had different gap ratios (G = 0.138 and 0.267), and one rig contained a central drive shaft, there was little difference between the measured Nusselt numbers. For the case of “increasing temperature distribution” (where the temperature of the disks increases radially), the local Nusselt numbers increase radially; for a “decreasing temperature distribution,” the Nusselt numbers decrease radially and become negative at the outer radii. For the increasing temperature case, a simple correlation was obtained between the local Nusselt numbers and the local Grashof numbers and the axial Reynolds number.

scholarly journals Heat Transfer in a Rotating Cavity With a Stationary Stepped Casing

1998 ◽  
Author(s):  
Iraj Mirzaee ◽  
Paul Quinn ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Flow Parameter ◽  
Rotating Disc ◽  
Flow Rates ◽  
Nusselt Numbers ◽  
Rotating Cavity ◽  
Wide Range ◽  
Heated Disc ◽  
Cooling Air

In the system considered here, corotating “turbine” discs are cooled by air supplied at the periphery of the system. The system comprises two corotating discs, connected by a rotating cylindrical hub and shrouded by a stepped, stationary cylindrical outer casing. Cooling air enters the system through holes in the periphery of one disc, and leaves through the clearances between the outer casing and the discs. The paper describes a combined computational and experimental study of the heat transfer in the above system. In the experiments, one rotating disc is heated, the hub and outer casing are insulated, and the other disc is quasi-adiabatic. Thermocouples and fluxmeters attached to the heated disc enable the Nusselt numbers, Nu, to be determined for a wide range of rotational speeds and coolant flow rates. Computations are carried out using an axisymmetric elliptic solver incorporating the Launder-Sharma low-Reynolds-number k-ε turbulence model. The flow structure is shown to be complex and depends strongly on the so-called turbulent flow parameter, λT, which incorporates both rotational speed and flow rate. For a given value of λT, the computations show that Nu increases as Reϕ, the rotational Reynolds number, increases. Despite the complexity of the flow, the agreement between the computed and measured Nusselt numbers is reasonably good.

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

Optimal energy growth in stably stratified turbulent Couette flow

2021 ◽  
Author(s):  
Grigory Zasko ◽  
Andrey Glazunov ◽  
Evgeny Mortikov ◽  
Yuri Nechepurenko ◽  
Pavel Perezhogin
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Couette Flow ◽  
Large Scale ◽  
Thin Layers ◽  
Plane Couette Flow ◽  
Turbulent Layer ◽  
Wide Range ◽  
The Mean ◽  
Optimal Disturbances

<p>In this report, we will try to explain the emergence of large-scale organized structures in stably stratified turbulent flows using optimal disturbances of the mean turbulent flow. These structures have been recently obtained in numerical simulations of turbulent stably stratified flows [1] (Ekman layer, LES) and [2] (plane Couette flow, DNS and LES) and indirectly confirmed by field measurements in the stable boundary layer of the atmosphere [1, 2]. In instantaneous temperature fields they manifest themselves as irregular inclined thin layers with large gradients (fronts), spaced from each other by distances comparable to the height of the entire turbulent layer, and separated by regions with weak stratification.</p><p>Optimal disturbances of a stably stratified turbulent plane Couette flow are investigated in a wide range of Reynolds and Richardson numbers. These disturbances were computed based on a simplified linearized system of equations in which turbulent Reynolds stresses and heat fluxes were approximated by isotropic viscosity and diffusion with coefficients obtained from DNS results. It was shown [3] that the spatial scales and configurations of the inclined structures extracted from DNS data coincide with the ones obtained from optimal disturbances of the mean turbulent flow.</p><p>Critical value of the stability parameter is found starting from which the optimal disturbances resemble inclined structures. The physical mechanisms that determine the evolution, energetics and spatial configuration of these optimal disturbances are discussed. The effects due to the presence of stable stratification are highlighted.</p><p>Numerical experiments with optimal disturbances were supported by the RSF (grant No. 17-71-20149). Direct numerical simulation of stratified turbulent Couette flow was supported by the RFBR (grant No. 20-05-00776).</p><p>References:</p><p>[1] P.P. Sullivan, J.C. Weil, E.G. Patton, H.J. Jonker, D.V. Mironov. Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer // J. Atmos. Sci., 2016, V. 73, P. 1815-1840.</p><p>[2] A.V. Glazunov, E.V. Mortikov, K.V. Barskov, E.V. Kadantsev, S.S. Zilitinkevich. Layered structure of stably stratified turbulent shear flows // Izv. Atmos. Ocean. Phys., 2019, V. 55, P. 312–323.</p><p>[3] G.V. Zasko, A.V. Glazunov, E.V. Mortikov, Yu.M. Nechepurenko. Large-scale structures in stratified turbulent Couette flow and optimal disturbances // Russ. J. Num. Anal. Math. Model., 2010, V. 35, P. 35–53.</p>

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