A

spiijS©

1

ssLlscfdr

sgSsdetl

0d

Nuclear Engineering and Design 237 (2007) 1025–1032

Investigation of mixed convection in a large rectangular enclosure

Fenglei Niu a, Haihua Zhao b, Per F. Peterson b,∗, Joel Woodcock c, Robert E. Henry d

a Condensed Matter and Thermal Physics Group MS K764, Los Alamos National Laboratory, Los Alamos, NM 87545, USAb Department of Nuclear Engineering, University of California, Berkeley, CA 94720-1730, USA

c Westinghouse Electric Company, Monroeville, PA 15146, USAd Fauske & Associates, Inc., Burr Ridge, IL 60527, USA

Received 25 August 2006; received in revised form 14 December 2006; accepted 15 December 2006

bstract

This experimental research investigates mixed convection and heat transfer augmentation by gaseous forced jets in a large enclosure, at conditionsimulating those of passive containment cooling systems for Gen III+ passively safe reactors. The experiment is designed to measure the key

arameters governing heat transfer augmentation by forced jets, and to investigate the effects of geometric factors, including the jet diameter, jetnjection orientation, interior structures, and enclosure aspect ratio. The tests cover a variety of injection modes leading to flow configurations ofnterest for mixing and stratification phenomena in containments under accident conditions. Correlations for heat transfer augmentation by forcedets are developed and compared with experimental data. The characteristic recirculation speed inside the enclosure is introduced and analyzed.

mula

1aKahornlmstliel

v

teady stratified temperature distributions are compared with model si2007 Elsevier B.V. All rights reserved.

. Introduction

Passive containment cooling systems (PCCS) provide theafety-related ultimate heat sink for a new generation of pas-ively safe reactors such as AP1000 and ESBWR. During aOCA accident, natural forces, such as gravity, natural circu-

ation, and a small number of automatic valves make the safetyystem work. The natural circulation and the pipe break injectionause the combined natural and forced convection heat trans-er in the containment. The steel containment vessel, in someesigns like the AP1000, provides the heat transfer surface thatemoves heat from inside the containment to the outside.

Mixed convection flows have received considerable attentionince the late 1970s, and comprehensive literature reviews wereiven by Incropera and Dewitt (1996). Fox et al. (1992) andmith et al. (1992) found that experimental results for transienttratification of BWR pressure suppression pools could be pre-icted using numerical solutions of one-dimensional differential

quations describing the effect of buoyant jets on the verticalemperature distribution. In University of California at Berke-ey, some mixed convection and related researches have since

∗ Corresponding author. Tel.: +1 510 643 7749; fax: +1 510 643 9685.E-mail address: peterson@nuc.berkeley.edu (P.F. Peterson).

ilaotMc

029-5493/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2006.12.011

tions of the BMIX++ code.

990s been performed for both gaseous and liquid fluids. Someccomplishments related to gas-jet mixed convection include:uhn et al. (2002) studied mixing processes and heat transfer

ugmentation by a hot-air jet in a large cylindrical enclosureeated from the bottom, and gave a correlation as a functionf Archimedes number, a fluid property factor, and a geomet-ic factor; Peterson et al. (1991) studied experimentally andumerically transient thermal stratification in pools with shal-ow buoyant jets; Peterson (1994) showed that large enclosures

ixed by buoyant plumes and wall jets can often be expected totratify, and provided a criterion for assessing when the momen-um injected by forced jets would break down stratification inarge enclosures; Peterson and Gamble (1998) presented a scal-ng method that could provide the basis for the design of scaledxperiments for studying jet-induced heat and mass transfer inarge enclosures.

Mixed convection is of interest and importance in a wideariety of engineering applications. However, mixed-convectionn large rectangular enclosures has not been investigated at greatength. Limited work has been performed on natural-convectionugmentation by forced jets. Few experimental data have been

btained on mixing and stratification phenomena inside largehree-dimensional enclosures agitated by forced-jet flows.

uch of the research has concerned laminar flow in simpleonfigurations and geometries. Many experiment geometries

1026 F. Niu et al. / Nuclear Engineering and

Nomenclature

A surface area (m2)Ar Archimedes numberb width parameter (m)C coefficientd jet diameter (cm)Dt diameter of the block tube (cm)GrL enclosure Grashof numberK empirical loss coefficientL enclosure characteristic length (m)m mass (kg)M momentum flux (kg m/s2)n unit normal vector to surfaceNu Nusselt numberP mechanical energy flux (kg m2/s3)r radial coordinate (m)Re Reynolds numberS surface area (m2)T temperature (K)u x-velocity (m/s)u′ fluctuating x-velocity (m/s)U velocity (m/s)V volume (m3)W mass rate (kg/s)X distance from jet entrance (m)z vertical coordinate (m)

Greek symbolsαT Taylor’s jet entrainment constantβ coefficient of thermal expansion (K−1)μ dynamic viscosity (N s/m2)ν kinematic viscosity (m2/s)ρ density (kg/m3)

Subscriptsa ambientb bulk valuebj free buoyant jetC centerlineD dragJ jetL using enclosure characteristic lengthm mixed convectionn natural convectiono jet outletR recirculation

aaEamc

hietoteibslfratai

2

tss

sotpcmcastihs

ccaeAiroamdpmenclosure.

w wall

re simplified into parallel-plate channels or rectangular cavitiesnd the thermal boundary conditions are set to be symmetrical.xtensive mixing experiments in large containment enclosure

re thus needed to improve key scaling, experimental, andodeling tools for predicting mixing and transport in passive

ontainments and confinement enclosures.ww

Design 237 (2007) 1025–1032

This experimental research studies mixed-convection andeat transfer augmentation by forced jets in various directionsnside a large enclosure with a vertical cooling surface. Thexperiments are performed by varying several geometric fac-ors, including the jet diameter, jet injection orientation, flowbstructions, and enclosure aspect ratio. The correlations of heatransfer augmentation by forced jets are developed and tested byxperimental data. The recirculation speed inside the enclosures defined and analyzed. The steady stratified temperature distri-utions are compared to the predictions made by BMIX++ codeimulation. Both scaling and modeling of stratified mixing inarge enclosures require detailed and accurate empirical modelsor wall and free jets. This research effort provides experimentalesults to support the development of a new, computation-lly efficient model for mixing under the stratified conditionshat characterize large volumes in passive systems, and forssessing the heat transfer augmentation produced by forced-jetnjection.

. Experimental facilities and test procedures

Fig. 1 shows a schematic diagram of the experimental sys-ems. They are an open loop composed of air supplies, heatingystems, a test section with a large insulated rectangular enclo-ure, cooling systems, and data acquisition.

The large rectangular enclosure was constructed with theize of 2.29 m × 2.29 m × 2.29 m. One of the walls was madef a 0.32-cm-thick copper plate. Cooling water was circulatedhrough copper tubes, welded to the backside of the copperlate, to generate a nearly isothermal surface. All the walls,eiling, and floor were surrounded with insulation materials,aking an adiabatic test section. The wall opposite the verti-

al cooling surface could be moved to change the enclosurespect ratio. The jet tubing inserted horizontally into the enclo-ure through this wall at different locations. The hot air enteredhe enclosure from the jet and left through a 53-mm i.d. open-ng at the bottom of the movable wall. Compressed air waseated by helical heaters before being injected into the testection.

Thermocouples and heat flux sensors were embedded in theopper plate to measure the temperature and heat flux of theooling surface. Some thermocouples were mounted in the inletnd outlet of the cooling water to measure the temperature differ-nce of the cooling water for the calculation of the cooling rate.

calibrated orifice with a differential pressure transducer wasnstalled in the cooling water loop to measure the water flowate. Heating rates by injected hot air were calculated basedn the flow rate and the temperature difference between their inlet and outlet. The air flow rate at inlet and outlet wereeasured using calibrated rotameters. The ambient temperature

istribution inside the enclosure was measured by thermocou-le matrix. The enclosure was looked as a control volume inass balance. There is no significant pressure change in the

To start the experiment, the water valves and the air valvesere slowly opened until the desired air and water flow ratesere reached. Heaters were turned on and checked regularly.

F. Niu et al. / Nuclear Engineering and Design 237 (2007) 1025–1032 1027

am o

Tada

ccte

3

3h

asctpi

t

wRt(

A

ws

f

N

wmdptti

hbwitiT1 at low Archimedes number, where heat transfer is dominatedby natural convection. It is found (more clearly for vertical/upinjection) that the experimental data, regardless of the jet diam-eter, are clustered into groups of trend lines in accordance with

Fig. 1. Schematic diagr

he heater outlet temperature should be monitored carefully tovoid overheating. When the temperatures inside the enclosureid not have significant changes for 15 min, the system achievedsteady state. Data were recorded every 10 s.

Experiments were first performed to investigate the naturalonvective heat transfer in the enclosure, and the results wereompared to those from combined natural and forced convec-ion. The natural circulation currents could develop in the largenclosure when the wall is cooled without jet injection.

. Experimental results and analysis

.1. Effects of injection orientation and jet diameter oneat transfer augmentation

To investigate how injection orientations and jet diametersffect heat transfer augmentation, air is injected into the enclo-ure with four directions: (A) horizontal injection toward theooling plate, (B) 45◦ upward injection, (C) vertical/up injec-ion, and (D) 180◦ backward injection away from the coolinglate. Three different size jet nozzles are employed for eachnjection direction.

As illustrated in Fig. 2, the experimental data for augmenta-ion can be well correlated by

Num

Nun= (1 + CJArJ)

1/3 (1a)

here the jet Archimedes number is a function of the jeteynolds number, ReJ = UJdJ/ν, ν is the kinematic viscosity of

he air, and the natural convection Grashof number, GrL = gβ

Tb − Tw)L3x/ν2:

Re2J

rJ =

GrLx

(2a)

here UJ is the jet velocity, dJ the jet diameter, and Lx the enclo-ure characteristic length. The temperature–average correlation

f experimental system.

or the natural convection is

un = C1Gr1/3Lx

Pr1/3

here C1 = 0.128. Eq. (1a) is the correlation of forced-jet aug-entation of natural convection heat transfer, which can be

erived using a combining rule for mixed convection and appro-riate forced and natural convection models. It is a function ofhe jet Archimedes number and the coefficient CJ, which is inhe range of 5.4–8.5 and includes the effects of the jet mode,njection orientation, and enclosure aspect ratio.

The magnitude of heat transfer augmentation is largest fororizontal injection toward the cooling plate (A), and followedy 45◦ injection (B), vertical/up injection (C), and 180◦ back-ard injection (D). Compared to vertical/up injection, horizontal

njection has better mixing effects, and the injection towardhe cooling plate can significantly increase the wall jet veloc-ty at the heat transfer surface, which in turn raises heat transfer.he data for all injection orientations asymptotically approach

Fig. 2. Effects of injection orientation and jet diameter.

1028 F. Niu et al. / Nuclear Engineering and

td

3a

sja

rtevrecdttttcct

3

wmtews

ibfie

rntedtf

u

wbi

wniE

pe

b

w

d

wid

bdt

Tjcmtfn

mt

Fig. 3. Effects of enclosure aspect ratio on heat transfer augmentation.

heir injection orientations, which implies that the effect of jetiameter is weak.

.2. Effects of enclosure aspect ratio on heat transferugmentation

Fig. 3 gives a comparison of the effects of varying the enclo-ure aspect ratio. Experiments were performed with vertical/upet injections in a large enclosure (2.11 m × 2.27 m × 2.18 m)nd a tall narrow enclosure (1.30 m × 2.27 m × 2.18 m).

It can be seen the heat transfer augmentation increases witheduction of enclosure aspect ratio. CJ is equal to 5.9, and 7.7 forhe large enclosure and medium enclosure, respectively. Somexperiments (Kuhn et al., 2002) have shown that the averageelocities in the enclosure induced by jet injection increase witheduction of enclosure aspect ratio, which can explain thesexperimental results. After the buoyant jet reaches the insulatedeiling, it transforms to a ceiling jet flow spreading out withecreasing velocity. In a large enclosure, due to the friction,he ceiling jet flow may dissipate completely before reachinghe vertical cooling plate. In the narrow enclosure, however,he ceiling jet flow could have sufficient kinetic energy to reachhe corner and then turn down to accelerate the wall jet on theooling surface, which will assist heat transfer between air andooling plate. So the smaller enclosure can receive higher heatransfer augmentation.

.3. Effects of obstructions on heat transfer augmentation

The experimental data from a simplified, empty enclosureill inevitably be quite different from those from a real contain-ent with complex pipes, stairways, and other interior structures

hat perturb large-scale recirculation flows. To investigate theffects of structures on heat transfer augmentation, experimentsere performed with some flow obstructions inside the enclo-

ure.Experiments were first performed with the jet directly

mpinging upon a 4.2-cm diameter cylinder, which was placedetween the jet nozzle and the cooling plate. With this con-guration, the cylinder experienced large drag forces and thusxtracted substantial momentum from the jet.

reto

Design 237 (2007) 1025–1032

If the jet hits a blocking structure such as the cylinder beforeeaching the opposite wall, the loss of jet momentum can sig-ificantly affect the effectiveness of the mixing, and thus reducehe heat transfer rate. Except for the small region near the jetxit or impinged surface, the jet will transit to become a fullyeveloped jet if it does not impinge on a blocking structure. Inhis region, the distribution of the streamwise velocity across aree expanded jet has been given by List (1982):

(r) = UC e−(r/b)2(3)

here UC is the local streamwise velocity at the centerline andthe width parameter. The fractional momentum loss due to

mpingement on a cylinder can then be evaluated by

Mloss

M= 2

∫∞0 CDρu2(r)/2Dt dr∫∞

0 ρu2(r)2πr dr(4)

here the drag coefficient is CD ≈ 0.9 in the range of Reynoldsumber of the experiments, Dt the diameter of the blocking tub-ng, and ρ the air density, assumed to be constant. Integratingq. (4) yields:

Mloss

M= CDDt√

2πb(5)

For a given self-similar distribution of mean velocity andressure, the width parameter b is related to the local jetxpanded diameter dbj (List, 1982):

= dbj

2√

2(6)

here dbj was given by Peterson and Gamble (1998):

bj = 4√

2αTx + dbj0 (7)

here αT is the Taylor’s jet entrainment constant, typically tak-ng a value around 0.05, dbj0 the jet nozzle diameter, and x is theistance between the jet exit and the obstruction.

Then from Eqs. (5)–(7) the fraction of momentum loss cane estimated in terms of the jet nozzle diameter, blocking tubingiameter, and the distance between the jet origin and the blockingubing, as

Mloss

M= 2CDDt√

π(4√

2αTx + dbj0)(8a)

his equation is only valid in the linear decay region far fromet exit and cooling plate. In the regions near the jet exit orooling surface, the flow field has large spatial variations thatake it complicated to estimate momentum loss. Eq. (8a) shows

he fraction of jet momentum loss increases with the projectedrontal size of the blocking structure and decreases with the jetozzle diameter and the distance from the jet origin.

Fig. 4 shows one of the experimental results. In this experi-ent, a 2.2 cm i.d. jet nozzle was used and the distance between

he jet exit and the cylinder was 30 cm. The experimental

esults were plotted compared to those from non-obstructionxperiments. The heat transfer augmentation decreased due tohe obstruction, giving CJ = 5.5, compared to CJ = 8.5 for non-bstruction experiment. This can be explained by the effect of

F. Niu et al. / Nuclear Engineering and Design 237 (2007) 1025–1032 1029

thn

A

f

M

t

tt

dItwatsd

3B

ddarP

F

v

vcsflFa(iesps

ewmswoe

ewooflheji

Fig. 4. Effects of large drag forces on heat transfer augmentation.

he obstruction on the jet Archimedes number. From Eq. (1a) theeat transfer augmentation is a function of the jet Archimedesumber:

rj = Re2j

GrL= ρ2u2

jd2bj0

μ2GrL(8b)

The jet momentum flux is conserved along the path of theree jet and can be expressed as

≡ ρπd2bj0u

2j

4(8c)

Eqs. (8b) and (8c) imply that, if density variation is neglected,he jet momentum is proportional to the jet Archimedes number:

Mloss

M∝ Arj,loss

Arj(8d)

So the loss of jet momentum due to obstruction will decreasehe jet Archimedes number, and therefore decrease the heatransfer augmentation.

The interior structures, even though not impinged by jetsirectly, can affect the mixed convection in the enclosure as well.n order to study the degradation of forced convection augmenta-ion due to the interior structures, 36 horizontal obstruction pipesere installed in four vertical arrays inside the enclosure, each

rray having nine pipes. Experiments were repeated to comparehe results with those from non-obstruction experiments. Fig. 5hows the heat transfer augmentation decreases by up to 20–30%ue to the flow obstructions.

.4. Steady temperature profile measurements andMIX++ code simulation

Stratification is the formation of horizontal layers of constantensity. Stratification exists in a containment atmosphere if the

ensity of the layers decreases in the upward vertical directionnd if forced convection mixing is not sufficiently strong to dis-upt the stable fluid layers. Based on the derivations provided byeterson (1994), a jet or plume is not able to disturb the stable

d(

w

ig. 5. Degradation of forced convection augmentation due to obstructions.

ertical stratification if:

ArJ

16<<

(1 + dbj0

4√

2αTL

)2

(9)

In parallel with experimental work, we have developed andalidated the BMIX++ code (Berkeley mechanistic MIXingode in C++) for predicting transient mixing in stratified enclo-ures. BMIX++ code is a one-dimensional Lagrangian transientow and heat transfer code. It is only used for low Arj cases.or high Arj, the enclosure is well mixed and can be treateds a lumped mass. By applying the Zuber scaling methodology1991), scaling rules were developed showing that under strat-fied conditions in an enclosure the governing conservationquations for mass, momentum, energy and species reduce toimpler one-dimensional forms (Peterson, 1994)—this scalingrovides the coupled, ordinary differential equations that areolved numerically by BMIX++.

The modeling of mixing and stratification in a large stratifiednclosure consists of two parts: modeling the ambient volume,hich can be calculated using a one-dimensional Lagrangianethod (tracking movable control volumes), and modeling sub-

tructures, such as the jets, plumes, and wall boundary flows,hich can be calculated with one-dimensional integral meth-ds or analytical methods. The two parts are coupled throughntrainment and discharge processes.

In each simulation of the experiments, four basic models aremployed in the BMIX++ code: free buoyant jet, isothermalall jet, small vent, and wall conduction models. Some sec-ndary effects, such as the ceiling jet caused by impingementf the free buoyant jet, wall jets along insulated vertical walls,oor jets caused by impingement of the wall jets, and radiationeat transfer, are neglected and contribute to differences betweenxperimental and model results. The direct interactions betweenets and walls are not considered because they typically are onlymportant at higher Arj, where the enclosure is well mixed. A

etailed description of the BMIX++ code can be found in Zhao’s2003).

Fig. 6 shows the temperature profiles for horizontal injectionith different jet inlet temperatures. The hot air was injected

1030 F. Niu et al. / Nuclear Engineering and

Ft

hw0baahlih

eccemibtld

3c

lflmflp

••••

Ttt

etliibIntc∫

Ed

U

s∫

ws

b

∫

wmflld

e

−

ejmTjm

ig. 6. Steady temperature profiles for experiment and BMIX++ code simula-ion: horizontal injection.

orizontally into the enclosure from a point near the movableall and at different elevations. A series of experiments with.14 m inlet diameter and 1/3 H inlet location were simulatedy the BMIX++ code. The cooling plate temperature was keptt approximately 15.5 ◦C and the inlet mass flow rate was keptt 0.004 kg/s. Two layers exist inside the enclosure: an almostomogenous cold lower layer and a linear stratified hot upperayer. The overall agreement between experiment and simulations acceptable, but the upper layer shape predicted by the codeas smaller gradient than the experimental shape.

The following neglected phenomena in BMIX++ code mayxplain the discrepancy between the experimental results and theode prediction. The free buoyant jet impinges directly on theooling plate. The heat transfer within the impingement zone isnhanced, but the heat transfer in the region above the impinge-ent zone is reduced because the upward wall jet driven by the

mpinging jet decreases the velocity of the downward naturaloundary flow along the cooling plate. Therefore, the simula-ion gives higher temperature just above the injection point andower temperature for the upper layer relative to the experimentalata.

.5. Empirical loss coefficients and recirculation speedorrelation

When a forced jet is injected into an enclosure, it induces aarge-scale recirculating flow due to the entrainment of ambientuid into the jet. These large-scale flows can augment heat andass transfer. Consideration of the strength of this recirculatingow can allow the heat and mass transfer augmentation to beredicted. Most of the jet kinetic energy is lost due to:

irreversible entrainment into the injected jet;turbulent flow losses in the corners;drag losses over structures;wall shear along enclosure surfaces.

he loss of jet kinetic energy by entrainment is relatively insensi-ive to the enclosure geometry, but the other losses depend uponhe speed of the large-scale recirculation flow induced in the

P

w

Design 237 (2007) 1025–1032

nclosure. The speed of this recirculation flow will adjust untilhe rate of kinetic energy injected by the jet is balanced by theseosses. The strength of this recirculating flow can be character-zed by a velocity scale. Here this characteristic velocity scales called the recirculation speed. The recirculation speed cane evaluated through an enclosure mechanical energy balance.f compression work is neglected, and the enclosure Reynoldsumber is large so that the Reynolds stress work is much largerhan the viscous stress work, a steady-status mechanical energyonservation equation for the enclosure can be given by

S

[n ·(

1

2ρu2u + pu

)]dS

+∫

V

(u · [∇ · u′u′])dV +∫

V

ρg(u · ez) dV = 0 (10)

q. (10) permits the recirculation speed for the enclosure to beefined as

2R = 1

m

∫V

(ρu2) dV (11)

The mechanical energy fluxes entering and leaving the enclo-ure across its surfaces can be represented by two terms:

S

[n ·(

1

2ρu2u + pu

)]dS = PE − PJ (12)

here PE is the mechanical energy flux leaving from the enclo-ure and PJ is the mechanical energy flux from the break jet.

Likewise, the volumetric mechanical energy sink terms cane expressed as

V

(u · [∇ · u′u′])dV = PD + PW +m∑

k=1

PS,k (13)

here PD is the mechanical energy dissipated by fluid entrain-ent in the break jet, PW the mechanical energy dissipated byow losses to the enclosure walls (both shear stress and form

osses in enclosure corners), and PS,k is the mechanical energyissipated by drag forces from flow over structures k = 1 to m.

Neglecting the buoyancy work, Eq. (10) can then bexpressed as

(PJ − PD) + PE + PW +m∑

k=1

PS,k = 0 (14)

If the jet does not impinge directly upon structures that wouldxperience large drag forces from the jet, the momentum of theet WJUJ is conserved. If the jet does impinge and loses someomentum, the loss can be treated with an empirical coefficient.hus, at the location where entrainment has equilibrated the

et mechanically with the large-scale recirculating flow, the netechanical energy delivered by the jet is

J − PD = KJ(WJ + Wentrained)U2R

2= KJWJUJUR

2(15)

here KJ is an empirical break-jet loss coefficient.

g and

P

lflic

P

wl

b

P

wtc

a(

Tcb

Sb

R

scft

w

A

o

aiteaafd

(fiic

KtgvAcKsadmef

3

The error analysis for the experiments was performed usingthe standard error propagation methods. The relative errors forall parameters can be calculated from the uncertainties of theapparatus and instruments used in the measurement. Table 2 lists

Table 1Optimal values of loss coefficients

Loss coefficients Optimal values

KJ 1.0 (no blocks); 0.3 (4.2 cm o.d. cylindera); 0(momentum diffusers)

KW 0.3 (1.7 m × 2.27 m × 2.18 m); 0.14(0.85 m × 2.27 m × 2.18 m)

F. Niu et al. / Nuclear Engineerin

For flow leaving the enclosure, the energy loss is

E = WJU2R

2(16)

Inside the enclosure, mechanical energy is dissipated by flowosses to walls and corners, as well as by drag forces due toow over structures. For a given enclosure geometry and break

njection orientation, flow losses to walls and corners can beorrelated empirically as

W = KWAWρaU3

R

2(17)

here AW is the wall surface area and KW an empirical enclosureoss coefficient.

Flow losses from drag forces due to flow over structures cane correlated empirically as

S,k = CD,kAS,kρaU3

R

2(18)

here AS,k is frontal area (the area projected perpendicular tohe recirculation flow) of structure k and CD,k an empirical dragoefficient.

With Eqs. (14)–(18), the enclosure mechanical energy bal-nce can then be written as

KWAWρa +m∑

k=1

CD,kAS,kρa

)(UR

UJ

)2

+ ρJAJ

(UR

UJ

)− KJρJAJ = 0 (19)

he second term of above represents the outflow energy loss thatan be neglected under low exit velocity. Then the relationshipetween the recirculation speed and jet velocity can be obtained:

UR

UJ=(

KJρJAJ

KWAWρa +∑mk=1CD,kAS,kρa

)1/2

(20)

o the recirculation Reynolds number and the jet Reynolds cane related by

eR,Lx = ReJ,dLxνJ

2νa

(πKJρJ

KWAWρa +∑mk=1CD,kAS,kρa

)1/2

(21)

The large-scale recirculating flow augments heat transfer tourfaces in the enclosure, and the strength of recirculating flowan be used as a parameter for correlating experimental data fororced-convection augmentation. Similar to Eq. (1a), the heatransfer augmentation can also be expressed as

Num

Nun= (1 + CRArR)1/3 (1b)

here the recirculation Archimedes number is defined by

2

rR = ReR

GrLx

(2b)

With Eqs. (1b), (2b), and (21), we can get the new expressionf the heat transfer augmentation:

Design 237 (2007) 1025–1032 1031

Num

Nun=[

1 + CRL2x

(νJ

νa

)2

×(

πKJρJ

KWAWρa +∑mk=1CD,kAS,kρa

)Re2

J,d

GrLx

]1/3

(22)

Eq. (22) gives the quantitative effects of injection conditionsnd enclosure geometry. KJ varies from 1.0 for jets which do notmpinge upon structures that generate significant drag forces,o a value approaching 0 for jets which are introduced into annclosure through highly effective momentum diffusers. KW isfunction of enclosure aspect ratio. The drag coefficient CD isfunction of Reynolds number and can take the empirical value

or flow over cylinders. CR is a strong function of the injectionirection.

Here, the empirical loss coefficients are estimated using Eq.20) and the data of heat transfer augmentation obtained here. Werst consider a large enclosure, which does not contain imping-

ng obstructions or interior structures. In this condition, Eq. (22)an be simplified into:

Num

Nun=[

1 + CRL2x

(νJ

νa

)2(πρJ

KWAWρa

)Re2

J,d

GrLx

]1/3

(23)

W is constant for the fixed aspect ratio and CR varies with injec-ion direction. We can find values for these parameters whichive the best correlation, using Eq. (23), for the experimentalalues of heat transfer augmentation that have been measured.fter finding CR for each injection direction, in the same way we

an continue to find each KW by changing enclosure aspect ratio,J by adding impinging obstructions, and CD by adding interior

tructures. Table 1 gives optimal values for the loss coefficientsnd Figs. 7–9 give plots of predicted values versus experimentalata of the heat transfer augmentation, which show good agree-ent. The heat loss from insulated walls was not included in the

xperimental data, which made the heat transfer rates obtainedrom experimental date consistently less than predicted values.

.6. Average relative errors

CD,k 1.2 (2 in. o.d. horizontal tubing)CR 300 (0◦ injection); 120 (45◦ injection); 100

(90◦ injection); 65 (180◦ injection)

a At 30 cm from the jet outlet.

1032 F. Niu et al. / Nuclear Engineering and

Fig. 7. Large enclosure, 0◦ injection, no blocks, no interior structures.

Fig. 8. Large enclosure, 0◦ injection, impinging a block, no interior structures.

Fig. 9. Large enclosure, 90◦ injection, no blocks, 36 interior pipes.

Table 2Average relative errors of major dimensionless parameters

Name Relative error (%)

Jet Reynolds number ±3.1Enclosure Grashof number ±8.7Average Nusselt number (natural convection) ±2.9Average Nusselt number (mixed convection) ±28.9Jet Archimedes number ±10.6Heat transfer augmentation ±29.1

tu

4

ujjirceotpatc

A

mattaHUh

R

F

I

K

LP

P

P

S

Z

Z

Design 237 (2007) 1025–1032

he average relative errors of major dimensionless parameterssed in the experiments.

. Conclusions

The experimental studies have investigated heat transfernder combined natural and forced convection with a variety ofet injection modes. The heat transfer augmentation by forcedets is controlled by jet Archimedes number, fluid properties,njection orientation, flow obstructions, and enclosure aspectatio. The experimental data are well correlated by developedorrelations. The strength of the recirculating flow inside thenclosure can be characterized by the recirculation speed. Theptimal empirical loss coefficients in the correlation of heatransfer augmentation were selected, and based on the selectedarameters, the predicted heat transfer augmentation valuesgree well with experimental data. For buoyant jets (low Arj)he steady stratified temperature distributions inside an enclosurean be predicted by BMIX++ code simulation.

cknowledgements

Funding for this research was provided by the U.S. Depart-ent of Energy (DOE) under the NEER Research Grant Program

nd by Westinghouse Electric Company, as part of the researcho improve understanding of mixing and heat transfer augmenta-ion by buoyant and forced jets in reactor containments. The firstuthor gratefully acknowledges all the members in the Thermal-ydraulics Laboratory, Department of Nuclear Engineering,niversity of California at Berkeley, who provided so much kindelp and made construction of the experimental facility possible.

eferences

ox, R.J., et al., 1992. Temperature distribution in pools with shallow buoyantjets. In: Proceedings of the Fifth International Topical Meeting on NuclearReactor Thermal Hydraulics (NURETH-5), September 21–24, Salt LakeCity, Utah, pp. 1227–1234.

ncropera, F.P., Dewitt, D.P., 1996. Fundamentals of Heat and Mass Transfer.John Wiley & Sons, New York, pp. 515–516.

uhn, S.Z., Kang, H.K., Peterson, P.F., 2002. Study of mixing and augmentationof natural convection heat transfer by a forced jet in a large enclosure. J. HeatTransfer 124 (4), 660–666.

ist, E.J., 1982. Turbulent jets and plumes. Ann. Rev. Fluid Mech. 14, 189–212.eterson, P.F., Rao, I.J., Schrock, V.E., 1991. Transient Thermal Stratification

in Pools with Shallow Buoyant Jets, Symposium on Nuclear Reactor Ther-mal Hydraulics. In: Hassan, Y.A., Hochreiter, L.E. (Eds.), Nuclear ReactorThermal Hydraulics, HTD-Vol. 190, ASME, New York, pp. 55–62.

eterson, P.F., 1994. Scaling and analysis of mixing in large stratified volumes.Int. J. Heat Mass Transfer 37 (1), 97–106.

eterson, P.F., Gamble, R., 1998. Scaling for forced-convection augmentationof heat and mass transfer in large enclosures by injected jets. Trans. Am.Nucl. Soc. 78, 265–266.

mith, B.L., et al., 1992. Analysis of single-phase mixing experiments in openpools. Thermal Hydraulics of Advanced and Special Purpose Reactors,ASME HTD-Vol. 209, pp. 91–100.

hao, H., 2003. Computation of mixing in large stably stratified enclosures.Ph.D. Dissertation. University of California, Berkeley.

uber, N., 1991. An Integrated Structure and Scaling Methodology for SevereAccident Technical Issues Resolution, Appendix D, NUREG/CR-5809, U.S.Nuclear Regulatory Commission.