Buoyancy-Induced Flow in Open Rotating Cavities

7/30/2019 Buoyancy-Induced Flow in Open Rotating Cavities

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J. Michael OwenUniversity of Bath,

Bath, BA2 7AY, UK

Hans Abrahamsson

Klas Lindblad

Volvo Aero Corporation,

46181 Trollhttan, Sweden

Buoyancy-Induced Flow in OpenRotating Cavities

Buoyancy-induced flow can occur in the cavity between the co-rotating compressor disks

in gas-turbine engines, where the Rayleigh numbers can be in excess of 1012. In mostcases the cavity is open at the center, and an axial throughflow of cooling air can interactwith the buoyancy-induced flow between the disks. Such flows can be modeled, compu-

tationally and experimentally, by a simple rotating cavity with an axial flow of air. Thispaper describes work conducted as part of ICAS-GT, a major European research project.Experimental measurements of velocity, temperature, and heat transfer were obtained ona purpose-built experimental rig, and these results have been reported in an earlier

paper. In addition, 3D unsteady CFD computations were carried out using a commercial

code (Fluent) and a RNG k- turbulence model. The computed velocity vectors andcontours of temperature reveal a flow structure in which, as seen by previous experiment-ers, radial arms transport cold air from the center to the periphery of the cavity, andregions of cyclonic and anticyclonic circulation are formed on either side of each arm.The computed radial distribution of the tangential velocity agrees reasonably well withthe measurements in two of the three cases considered here. In the third case, the com-

putations significantly overpredict the measurements; the reason for this is not under-stood. The computed and measured values of Nu for the heated disk show qualitativelysimilar radial distributions, with high values near the center and the periphery. In two ofthe cases, the quantitative agreement is reasonably good; in the third case, the compu-

tations significantly underpredict the measured values. DOI: 10.1115/1.2719260

1 Introduction

Figure 1 shows a simplified diagram of a high-pressure com-

pressor rotor through the center of which is an axial flow of air

that is used downstream for turbine cooling. When the cooling air

has a lower temperature than the rotating surfaces as is the casefor steady-state engine operation , buoyancy-induced flow can oc-

cur in the cavity between the disks.In contrast to the open cavity considered above, in some en-

gines the cavity is closed: the air is enclosed by the rotating disksand by inner and outer cylindrical surfaces. For the case where the

outer surface is hotter than the inner one, King et al. 1 showedthat Rayleigh-Bnard convection could occur, as shown in Fig. 2.For a rotating inviscid fluid, a radial velocity is only possible ifthere is a circumferential gradient of pressure; without this, the

flow would be thermally stratified and convection could not takeplace. Counter-rotating cyclonic and anticyclonic vortices, withtheir axes parallel to the axis of rotation, respectively, create re-

gions of low and high pressure; these provide the circumferentialpressure gradients that allow convection to occur.

The main features of the flow in the open system can be mod-eled by the simplified rotating cavities shown in Fig. 3. Most of

the experimental work to date has been conducted with either acentral inlet or with an annular inlet for the cooling air. In thelatter case, the inner cylinder rotates at the same speed as thedisks; in an engine, it usually rotates at a slower speed. In the

open cavities, the axial throughflow tends to induce a toroidalcirculation near the center, and buoyancy-induced flow occurs atthe outer radii.

An experimental project on an open cavity has recently been

published 2 . The work was carried out as part of a major Euro-pean research project, entitled The Internal Cooling Air Systemsof Gas Turbines ICAS-GT . The project, which was sponsored

by the European Commission, ran from 1998 to 2000 and in-volved ten gas turbine companies and four universities. The Uni-versity of Bath carried out experiments in a rotating cavity with anannular inlet as shown in Fig. 3 b , and Volvo Aero Corporationconducted computations of the flow in the system.

This paper describes the computational method used and pre-sents comparisons between the computed and measured results.The principal objectives are to improve the understanding of thesecomplex rotating flows and to see if CFD codes are capable ofproviding predictions that could be used in the design of internal-air systems in gas turbines.

Section 2 is a brief review of some relevant research; Sec. 3describes the experimental apparatus; Sec. 4 outlines the compu-tational method; and Sec. 5 discusses comparisons between com-putations and measurements. The principal conclusions are sum-marized in Sec. 6.

2 Review of Previous Work

Although the paper concentrates on open cavities, it is useful toconsider some of the published research on closed systems. Bohnet al. 36 made heat transfer measurements in a sealed rotatingannulus with a/b =0.35 and 0.52 where the heat flow could beeither axial from a hot to a cold disk or radial from a hot outercylinder to a cold inner one . For the radial case, they correlated

their Nusselt number, for Rayleigh numbers up to 1012, by Nu

Rac, where the constant c was approximately 0.2. Sun et al. 7used an unsteady 3D CFD code, with no Reynolds averaging orturbulence model, to compute the flow in a sealed annulus with aradial heat flow. Their computed Nusselt numbers were in goodagreement with the correlations of Bohn et al.

King et al. 1 used unsteady 2D and 3D CFD codes, with noReynolds averaging, to compute the heat transfer in a sealed an-

nulus with a radial heat flow for Ra 109. The computed stream-lines showed that Rayleigh-Bnard convection occurred, with cy-

clonic and anticyclonic vortices in the r- plane. The time-averaged Nusselt numbers were in good agreement withcorrelations for a stationary cavity with the gravitational accel-

Contributed by the International Gas Turbine Institute of ASME for publication in

the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June

19, 2006; final manuscript received January 11, 2007. Review conducted by Dilip R.Ballal. Paper presented at the ASME Turbo Expo 2006: Land, Sea and Air GT2006 ,

May 811, 2006. Barcelona, Spain. Paper No. GT2006-91134.

Journal of Engineering for Gas Turbines and Power OCTOBER 2007, Vol. 129 / 893

Copyright 2007 by ASME

Downloaded 26 Jul 2010 to 202.88.225.67. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm


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eration replaced by the centripetal acceleration , but they weresignificantly higher than the correlations of Bohn et al.; the reasonfor this overestimate of Nu was not understood.

The Sussex group 813 made measurements and computa-tions for an open cavity with a/b0.1 with an axial through-flow of cooling air. There was no central shaft or cylinder, and theouter cylindrical surface and/or the disks could be heated.

Farthing et al. 8 carried out flow visualization and LDA laser-Doppler anemometry studies in both isothermal and heated cavi-

ties. In isothermal cavities 14 with large gap ratios G 0.4 , the

axial throughflow generated a powerful toroidal vortex, thestrength of which decreased as the Rossby number Ro decreased.

Depending on the values of G and Ro, axisymmetric and non-

axisymmetric vortex breakdown were observed in the central jet.When one or both of the disks were heated, the flow in the

cavity became non-axisymmetric, and cyclonic and anticyclonicvortices were observed, as shown schematically in Fig. 4. Farthinget al. used the so-called linear equations for rotating flows toexplain that, as stated above, the cyclonic and anticyclonic circu-lation generated the circumferential pressure gradient that isneeded to produce a radial flow inside the core of fluid betweenthe disks. In particular, they observed a radial arm that con-vected cold air from the center to the periphery of the cavity. The

core of fluid precessed at an angular speed c say slightly lessthan that of the disks; the ratio of c/ decreased as the tempera-ture difference between the disks and the cooling air increased.

Owen and Powell 2 made measurements in an open cavity,where a/b =0.4 and G =0.2, in which one of the disks was heated.

LDA and heat transfer measurements were made for 1.4 103

Rez 5 104 and 4 105 Re 3.2 10

6. Spectral analysisof the LDA measurements revealed a multicell structure compris-ing one, two, or three pairs of vortices. As found in the experi-ments of Farthing et al., the core of fluid between the disks pre-

cessed at an angular speed, c, less than that of the disks, and

c/ decreased as the temperature of the heated disk increased.

At the smaller values of Rez, the measured Nusselt numbers wereconsistent with buoyancy-induced flow; at the larger values of

Rez, the effect of the axial throughflow became dominant.Tian et al. 15 computed the flow and heat transfer in a rotating

cavity based on the geometry of Farthing et al. Their 3D, steady,turbulent computations showed that the flow structure comprisedtwo parts: Rayleigh-Bnard convection at the larger radii, andforced convection in the central region. The computations sug-

gested that there is a critical Rayleigh number above which theflow becomes unstable and time dependent.Johnson et al. 16 investigated the stability characteristics of

variable-density swirling flow in rotating cavities. Using anarrow-gap approximation for inviscid flow, they produced crite-ria for the necessary and sufficient conditions for stability. Whenthe rotating surfaces are colder than the cooling air such as attake-off in an aeroengine the flow is stably stratified: the axialthroughflow cannot penetrate very far into the cavity and the re-sulting convective heat transfer is relatively low. Conversely,when the rotating surfaces are hotter than the air at cruise andlanding , the flow is unstable, the axial flow can readily enter thecavity, and the heat transfer is increased as a consequence.

Fig. 1 Simplified diagram of high-pressure compressor rotorwith axial throughflow

Fig. 2 Rayleigh-Bnard vortices in a closed rotating cavity

Fig. 3 Rotating cavity with axial throughflow of cooling air

Fig. 4 Schematic of flow structure in a heated rotating cavitywith an axial throughflow of cooling air

894 / Vol. 129, OCTOBER 2007 Transactions of the ASME



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3 Experimental Setup

The experimental apparatus and instrumentation are described

below; more details are given in 2 .

4 Experimental Rig

The Bath rotating-cavity rig is shown in Fig. 5. The salient

dimensions of the cavity were a =150 mm, b =371 mm, r

=4.8 mm, and s =75.2 mm xa = a/b =0.40, G = s/b =0.20 .The downstream disk was made from 10 mm thick steel, the

back face of which was radiantly heated by a 21 kW stationaryelectric heater, and the front cavity-side face was covered by a1 mm thick glass-fiber mat in the outer surface of which ten RDFfluxmeters and ten thermocouples were embedded. The upstream

disc, which was 12 mm thick, was made from transparent poly-

carbonate. The outer shroud was made from 5 mm thick glass-fiber composite, the inner surface of which was thermally insu-

lated by a 5 mm thick layer of Rohacell foam. The inner cylinder,which was made from Rohacell foam, rotated synchronously withthe two disks and the shroud. So-called cobs, also made fromRohacell foam, were attached to the two disks; the cobs crudelymodeled the geometry of compressor disks, and they also pro-vided annular passages at inlet to and outlet from the cavity toencourage the air to enter and leave in the axial direction.

The rotating cavity and heater unit were enclosed by a station-ary steel casing, designed to withstand a differential pressure of 3bar. A window, in the upstream side of the casing, provided opticalaccess for LDA measurements. Cooling air for the cavity, andpressurising air for the outer casing, was supplied by a Bellis &

Morcom compressor with a maximum output of around 1 kg/s at4 bar absolute pressure. The cooling air was supplied, via station-ary piping and an inlet volute, into the annular space between therotating inner and outer tubes. The air then flowed radially out-ward through the axial and radial clearances between the rotatinginner cylinder and the upstream disc. After flowing axiallythrough the cavity, the air left the system, via the axial clearancebetween the inner cylinder and the downstream disk, through therotating inner tube from where it flowed into a stationary tube.Radial vanes, attached to the upstream and downstream radialfaces of the inner cylinder, ensured that the air entered the systemwith solid-body rotation.

Owing to stress considerations, the maximum speed of the

polycarbonate disk was limited to 1500 rev/min. The cavity wasrotated by means of a combination of two thyristor-controlled dc

motors not shown in Fig. 5 , with a total output of 26 kW, and

the rotational speed of the cavity could be controlled to

1 rev/ min. A toothed-belt and pulley system was used to transferthe power from the motors to the upstream and downstream discs;a layshaft ensured corotation of the two disks.

5 Instrumentation

As stated above, there were ten thermocouples and ten fluxme-ters on the front cavity-side surface of the heated downstreamdisk. Owing to failures, and to the fact that insulating foam cov-ered some of the instrumentation, not all the fluxmeters were ser-viceable. The signals from the rotating instrumentation werebrought out through a 52-channel silver/silver-graphite slip-ringunit. The voltages were then measured using a computer-controlled solartron data-logger and digital voltmeter with a reso-

lution of 1 V. The uncertainty of the thermocouple measure-ments was estimated to be 0.3C. It was necessary to correct themeasured heat fluxes for radiation from the heated disk to theunheated surfaces. Owen and Powell 2 suggested that their ap-proximate black-body correction could result in an overestimate inthe Nusselt numbers; a positive bias of Nu 50 could occur in theresults presented here.

The temperatures of the air at inlet to and outlet from the sys-tem were measured using total-temperature probes inserted in thestationary tubing upstream and downstream, respectively, of therig. The voltage outputs from the total-temperature probes weremeasured using the data-logger. No instrumentation was attached

to the shroud or to the inner cylinder, both of which were sensiblyadiabatic, or to the polycarbonate disk, which was quasi-adiabatic.

The flow rates of the cooling air and sealing air were measuredusing orifice plates made to British Standards BS1042, and the

estimated uncertainty was 3% of the measured flow rate. Theabsolute pressures of the air, and the pressure drop across theorifice plates, were measured using a pair of absolute and differ-ential pressure transducers multiplexed by a Scanivalve system,the outputs of which were recorded on the data-logger.

The LDA system used a 4W Spectra-Physics argon-ion laser,the beam of which was transmitted to the optics through a fibre-optics cable with an efficiency of around 50%. The TSI optics,which were configured in a single-component back-scatter mode,

were mounted on an x-y traversing table, allowing movement inthe radial and axial directions. By turning the transmitting optics

through 90 deg, it was possible to measure either the radial or thetangential component of velocity. The transmitting optics included

a Bragg cell, which allowed frequency shifts of up to 40 MHz,

and the beam spacing was 50 mm, which, with a 250 mm focal-

length lens, produced an optical probe volume around 1.4 mm

long and 0.14 mm diameter. The Doppler signal from the receiv-ing optics was processed by a TSI IFA-750 burst-correlator, which

could handle frequencies up to 90 MHz with signal-to-noise ratios

as low as 5 dB. Micron-sized oil particles for the LDA measure-ments were injected into the cooling-air supply upstream of therotating tubes in the rig. The estimated uncertainty in the velocity

measurements was 0.01r.

6 Computational Method

The geometry and computational mesh for the Bath rig isshown in Fig. 6. The final mesh had a total of 2,600,000 cells,

with 6500 in the r-z plane and 400 in the tangential direction. Amesh study showed that it was important to have many cells in the

tangential direction in order to resolve the thin radial armsreferred to above. Nonuniform grid spacing was used to ensure

that the values of y+ for the grid points nearest the walls were lessthan unity.

The 3D unsteady compressible CFD simulations were com-puted, in the rotating frame of reference, using the commercialCFD code Fluent with a segregated implicit solver SIMPLE .Second-order space-discretization, PRESTO pressure-discretization, and second-order implicit time-stepping were used.

Fig. 5 Schematic of Bath rotating-cavity rig




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The renormalized group RNG k- turbulence model was cho-sen, and different time steps and numbers of subiterations per timestep were investigated. Before starting to collect results, the com-

putation was run for a significant time, monitoring the integratedheat flux on the heated wall, to ensure that the final solutions wereindependent of the initial conditions.

The CFD analysis was run on a Linux PC cluster of 8 to 16CPUs, and the computations took about 1 week to complete.

7 Computational Results

The CFD analyses were performed for the three experimental

cases given in Table 1, and the radial distributions of T where

T= Ts Ti for the heated disk are shown in Fig. 7.

Figures 8 and 9 respectively show computed contours of Tc where Tc = Tc Ti in the mid-axial r- plane, at z/s =0.5, forexperiments 2 and 5. It should be noted that, as discussed below,the flow patterns changed with time, and the contours and vectorsshown in Figs. 813 were the final ones computed.

It can be seen in Fig. 8, for experiment 2, that the axial through-flow of cooling air creates a circular ring of cold fluid colored

Fig. 6 Geometry and grid of CFD model

Table 1 Test matrix for the experiments

Experiment 106 Rez 104 Ro

2 0.430 0.303 0.6745 1.57 0.164 0.1006 1.63 0.295 0.173

Fig. 7 Radial distribution of T K for heated disk

Fig. 8 Computed contours of Tc K in mid-axial plane forexperiment 2 Re/ 10

6 =0.43, Rez/ 104 =0.303




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blue at the center of the cavity. Radial arms green , similar to theone shown in Fig. 4, transport some of the fluid from the center to

the periphery of the cavity, creating a thin layer of cold air greenadjacent to the unheated shroud. For experiment 2, two distinctradial arms are clearly visible, and this is in agreement with thetwo-cell structure that was observed experimentally. To the rightof each radial arm is a region of high temperature red , which, asdiscussed below, is caused by air that is convected from the heateddisk into the fluid core.

The contours for experiment 5 in Fig. 9 are more complex.Several large and small radial arms can be seen, and to the right ofeach one is a high-temperature region. For this case, the experi-mental observations were unable to determine the number of cells.It is interesting to observe that the ring of cold air that can be seennear the center of Fig. 8 for experiment 2 is much larger than thatin Fig. 9 for experiment 5. This is consistent with the findings ofFarthing et al. 8 that the radial extent of the toroidal vortex,created by the throughflow, decreased as Ro decreased: for experi-

ments 2 and 5, Ro0.674 and 0.100, respectively.Figures 10 and 11 show the computed velocity vectors, in the

mid-axial r- plane, corresponding to the temperature contoursdiscussed above. Some streamlines are superposed on the vec-

tors so that the general flow structure can be seen more clearly.Colored contours, corresponding to the magnitude in m/s of thevectors, are used to show regions where the velocity is large rela-

tive to the rotating disks.The radial outflows that separate regions of cyclonic and anti-

cyclonic circulation in Fig. 10 correspond to the radial armsshown in Fig. 8. Although it cannot be seen from this figure, theaxial width of the radial arms is the same as the spacing betweenthe two cobs. To the right of the radial arms the circulation iscyclonic which, as noted by King et al. 1 , corresponds to aregion of low pressure in the core. In this region, air flows axiallyfrom the heated disk into the core, raising the temperature of thefluid in the mid-axial plane, as shown in Fig. 8. Conversely, in theanticyclonic zones to the left of the radial arms, the high pressurewill create an axial flow towards the heated disk.

In a stationary fluid, a vertical plane plume of hot air createsvortices on either side. In a rotating fluid, a radial plume, or radialarm, of cold air creates a cyclonic and an anticyclonic vortex on

either side and, as stated above, these vortices produce the circum-ferential gradient of pressure needed for the plume to penetrateradially into the rotating fluid. In Fig. 9, several embryonic radialarms can be seen, each with its associated pair of vortices, cir-

Fig. 9 Computed contours of Tc K in mid-axial plane forexperiment 5 Re/ 10

6 =1.57, Rez/ 104 =0.164

Fig. 10 Computed velocity vectors in mid-axial plane for ex-periment 2 Re/10

6 =0.43, Rez/ 104 =0.303

Fig. 11 Computed velocity vectors in mid-axial plane for ex-periemt 5 Re/10

6 =1.57, Rez/ 104 =0.164

Fig. 12 Computed contours of Nusselt number for experiment2 Re/10

6 =0.43, Rez/ 104 =0.303




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cumferentially to both left and right. There are also large values ofNu in Fig. 12 near the center where the axial throughflow im-

pinges on the heated disk. Owing to the more complex flow struc-ture in experiment 5, the similarity between the contours in Figs.9 and 13 is less obvious.

Figures 14 and 15 show a time-sequence of computed contours

of Tc in the mid-axial plane for experiments 2 and 5, respec-tively. The temperature scale for the contours is the same as thatshown in Figs. 8 and 9.

In Fig. 14 it can be seen that, although the overall flow structureis virtually invariant with time, the two radial arms rotate in theopposite sense to the rotation of the disks. This is consistent withthe experimental measurements, in a stationary frame of refer-ence, which show that the core of fluid rotates at a slower speedthan the disks. Figure 15 shows that the core of fluid for experi-ment 5 rotates in the opposite sense to the disks, but the overall

flow structure varies more with time than that for experiment 2.Figure 16 shows the comparison between the computed and

measured radial distribution of V/r in the mid-axial plane forexperiments 2, 5, and 6. It should be noted that the measuredvelocities at a fixed radius were time-average values in a station-ary frame of reference; as the core was rotating, these measuredvalues were, in effect, both time and circumferential averages. Thecomputations were made in the rotating frame, and the displayedvelocities are circumferential averages at the last time step; thecomputed circumferential averages were found to agree well withtime averages.

Bearing in mind the 1% uncertainty in the measured velocities,the computed distributions for experiments 2 and 6 show reason-able agreement with the measurements. The measured velocities

of Farthing et al. 8 showed that V/r 1 in the core of anisothermal cavity and, as a result of the toroidal vortex, which is

discussed above, a maximum value of V/r occurred near thecenter of the cavity, and this maximum value decreased as Rodecreased. This effect is consistent with the computations shown

in Fig. 16: a computed maximum in V/r occurs near the center

x=0.4 for experiment 2, where Ro0.674, but not for experi-

ments 5 and 6, where Ro0.100 and 0.173, respectively.The measured velocities for experiment 5 are significantly

smaller than the computations. In the experiments of Farthing et

al. 8 , the values of V/r at the larger radii of the heated cavitywere mainly greater than 0.9. This was the also the case foraround half of the 24 experiments reported by Owen and Powell 2 . In the other half, the measured values were similar to thoseshown in Fig. 16 for experiment 5, and these unusually low values

for the core rotation did not appear to correlate with Re, Rez, orRo. The differences between the computations and measurementsfor experiment 5 are not understood: either there were unknownexperimental errors in the measurements or the low values werecaused by a physical phenomenon, such as vortex breakdown, thatwas not captured by the computations.

Figure 17 shows the comparison between the computed andmeasured radial distribution of Nu for experiments 2, 5, and 6.The measured values of Nu were time-average values made byfluxmeters located at fixed locations on the rotating heated disk.

Fig. 13 Computed contours of Nusselt number for experiment5 Re/ 10

6 =1.57, Rez/ 104 =0.164

Fig. 14 Computed time-sequence of contours of Tc in mid-axial plane for experiment 2 Re/10

6 =0.43, Rez/ 104 =0.303.

Time in ms.

Fig. 15 Computed time-sequence of contours of Tc in mid-axial plane for experiment 5 Re/10

6 =1.57, Rez/ 104 =0.164.

Time in ms.




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The computed values represent circumferential space averages ofthe last time step; the computed circumferential averages werefound to agree well with time averages.

In all three cases, the computations and measurements showsimilar qualitative radial distributions: the higher values of Numeasured near the center and shroud are captured by the compu-tations. As stated above, the measured Nusselt numbers could bebiased by the approximate radiation correction; this could result ina significant experimental overestimate of the true values of Nu.Bearing in mind the experimental uncertainties, the quantitativeagreement is reasonably good for experiments 2 and 5, but thecomputations significantly underpredict the measurements for ex-periment 6; the underprediction is much greater than the maxi-mum bias Nu50 in the measured values of Nu. It is possiblethat a conjugate solution, taking account of the radiation to and

from the heated disk, could produce more accurate computationsof Nu, but this has yet to be tried.

8 Conclusions

3D unsteady CFD analysis of the flow and heat transfer in a

rotating cavity with an axial throughflow of cooling air have been

performed using a commercial CFD code Fluent incorporating

an RNG k- turbulence model. The CFD results have been com-

pared with velocity and heat transfer measurements made in a

rotating cavity rig in which one of the two disks was heated.

The computed contours of temperature and velocity vectors re-

veal a flow structure in which, as seen by previous experimenters,

radial arms transport cold air from the center to the periphery of

the cavity, and regions of cyclonic and anticyclonic circulation are

formed on either side of each arm. In the regions of cyclonic

circulation, where the pressure is low in the core, axial flow from

the hot disk creates regions of high temperature in the core. Theimpingement of the radial arms on the shroud, and of the axial

Fig. 16 Computed and measured radial distributions of V/r in mid-axial plane for experi-ment 2 Re/10

6 =0.43, Rez/ 104 =0.303, experiment 5 Re/ 10

6 =1.57, Rez/104 =0.164, and ex-

periment 6 Re/ 106 =1.63, Rez/ 10

4 =0.173

Fig. 17 Computed and measured radial distributions of Nu for experiment 2 Re/ 106 =0.43, Rez/10

4 =0.303, experiment 5Re/10

6 =1.57, Rez/ 104 =0.164, and experiment 6 Re/ 10

6 =1.63, Rez/ 104 =0.173




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throughflow on the central region of the heated disk, creates re-gions of high heat transfer at the large and small radii of the disk.

The computed radial distribution of V/r at z/s =0.5 agreesreasonably well with the measurements in two of the three casesconsidered here. In the third case, the computations significantlyoverpredict the measurements; the reason for this is not under-stood.

The computed and measured values of Nu for the heated diskshow qualitatively similar radial distributions, with high valuesnear the center and the periphery. In two of the cases, the quanti-tative agreement is reasonably good. In the third case, the compu-

tations significantly underpredict the measured values.The research has been successful in helping to understand theflow physics, but more work is required before the engine de-signer can depend solely on CFD codes to predict buoyancy-induced flow in rotating cavities.

Acknowledgment

The authors wish to acknowledge the support of the other con-sortium partners in the ICAS-GT project and to thank the Euro-pean Commission for helping to fund this work. We also thankJon Powell for obtaining the experimental measurements used inthis paper and Per Birkestad for help with some of the computa-tions. We are also grateful to the reviewers for their helpful andconstructive comments.

Nomenclaturea inner radius of cavity radius of inner cylinderb outer radius of cavity

d diameter of circular inlet

g acceleration

G s/b, gap ratioGr gL3T/2, Grashof number

k thermal conductivity

L characteristic length

m mass flow rate

n number of vortex pairsNu qL/kT, Nusselt numberPr /, Prandtl number

q heat flux

r

radiusRa PrGr, Rayleigh number

Re b2/, rotational Reynolds number

Rez WL/, axial Reynolds numberRo W/a, Rossby number

s axial gap between disks

t time

T absolute static temperature

Tc temperature in core at z/s =0.5

Ti inlet temperature

Ts surface temperature of heated disk

Vr, V radial, tangential components of velocity instationary frame of reference

W bulk-average axial velocity at inlet

x r/b, nondimensional radius

xa a/b, radius ratio of cavity

z axial distance from heated disk

thermal diffusivity Ti

1, volume expansion coefficient

r radial clearance between disks and innercylinder

T Ts Ti, disk temperature difference

Tc Tc Ti, core temperature difference

dynamic viscosity tangential coordinate kinematic viscosity

density

angular speed of cavity

c angular speed of air

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