Influence of a local obstruction of heat transfer in packed beds

POR FLUID

DYNAMICS

TECUNfSCftE

HOGESCftOet

Dun

VUEGTUIGD0UW~lJNmi TECHNICAL NOTE 80 B!~UOi1lEEK

1 3

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197~

INFLUENCE OF A LOCAL OBSTRUCTION ON HEAT TRANSFER IN PACKED BEDS

BY

J.J. GINOUX C. JOLY

RHODE-SAINT-GENESE, BELGIUM

TN 80

INFLUENCE OF A LOCAL OBSTRUCTION

ON HEAT TRANSFER IN PACKED BEDS by J.J. GINOUX C. JOLY May 1972

Th-i.4 WOltR. WM c.onduc.ted ~Olt the "Ga~ Cooled Blteedelt Reac.tolt

A~,ó 0 c.-i.at-i. 0 n " and pit e~ ent ed at th e Th eltm 0 h ydltau.l-i.~ S p ec.-i.al.i.~-t

Meet.i.ng at W-i.nd4c.ale on May

11-19, 1912,

.i.n c.onnec.t.i.on w.i.th the ENEA

GCFR

Pltogltamme.

TABLE OF CONTENTS Table of Contents •••••••••••••••••••••••••••••••••••• ~ Notations

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Summary •••••• " ••••••••••••••••••••••••••••••••••••••• ~11 Introduction _{• •}

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_{• • • • • •} 1 Test facility ••.•.•••.•••.•••••••••••••••••••••.••••• 3

Heat transfer measuring technique ••••••••••••••••••••

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Measurement of average values ••••••••••••••••••••••••

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Heat transfer distributions ,

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Preliminary measurements ••••••••••••••••••••••••••••• 8

Results

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Average heat transfer _{• • •}

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Heat _{transfer distribution • •}

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Conclusions

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10 10 11 12 Acknowledgments •••••••••••••••••••••••••••••••••••••• 12

NOTATlONS A, B n T s Tg óT = T_s

-

_Tg Cp Q k h Nu Re Pr - 1.1.

-constant values depending upon type of obstruction and Reynolds number range particle diameter

number of contact points between a sphere and surrounding spheres kinematic viscosity

superficial velocity : fluid velocity upstream the packed bed

surface temperature of a sphere coolant gas temperature

driving temperature

specific heat at constant pressure hea.t flux

thermal conductivity

hea.t transfer coefficient

Nüsselt number defined by Nu

=

~~P

Reynolds number defined by Re

=

V_o

~

Prandtl number defined by Pr

=

~~P

m m2/sec m/sec kcal/kSo Kcal/se kcal/mse

SUMMARY

The purpose of this study is to find the influence of a local Obstruction on heat transfer between one particle ~n a p packed bed and the coolant gas which is forced through i t .

A method ~s chosen and developed, giving average as well as local heat transfer coefficients in the case of a packed bed containing spherical particles of constant diameter.

The results show

- an important decrease of the average cooling of a sphere near the obstruction. The measurements can be correlated by an expression such as

B

Nu

=

A.Re

where Nu is the Nusselt number, Re the Reynolds number and A, B constants depending upon the type and the amount of obstruction.

- important local variations of the heat transfer coefficient over the surface of a spherp..

INTRODUCTION

In the gas cooled thermal reactor field, fuel development has moved towards coated fuel particles, using packed systems.

This advanced technology leads to higher heat fluxes so

that for a given power more compact reactors seem to be feasible.

A great amount of research has already been carried out ~n

different laboratories but a few problems remain to be solved.

For example, retention of dust from the coolant gas by the packed bed or fuel particle ruptures can produce local obstruc-tion whose effect on heat transfer is still unknown.

If the cooling of the part ic les near an obstruction is lar-gely decreased, the safety of the reactor may be compromised.

The purpose of our study is to find the influence of such an obstruction on heat transfer between one element in a packed bed and the coolant gas which is forced through it.

In the first section, the test facilities are described and the geometrical characteristics are justified.

Then th~ principle of the heat transfer measuring technique

~s explained. It is a steady state method with which average as weIl as local heat transfer coefficients can be measured.

In the final section, the results are summaried and discussed, showmg the importance of an obstruction on ree~t transfer in a

- 2

-Some of the material presented here is discussed 1n more details in reference

(1).

Le prix 1971 de la Société Royale Belge des lngénieurs et des lndustriels a été attribué à ce travail.

(1)

"Transfert de chaleur dans un empilement compact en présence d'un blocage" - Etude bibliographique et Expérimentale par C. Jo ly.

Université Libre de Bruxelles - lnstitut von Karman Septembre 1971.

2. TEST FACILITY

A schematic diagram of the test facility is shown 1n figure 1.

Air delivered by high pressure reservoirs passes through a regulating valve which maintains a constant and adjustable stagnation pressure upstream of the facility. The mass flow is measured by a diaphragm.

The air enters a settling chamber, the purpose of which is to produce a uniform flow at the entrance of the test section.

By using a 50 mm thick layer of packed particles of 5 mm diameter, followed by a wool screen and an honeycomb, the maximum

velocity variations in a cross section were maintained smaller

than about 10

%

of the mean velocity.

The square test section (563 mm x 563 mm) contains a packed

bed, of spherical elements of constant diameter, which simulates the core of a nuclear reactor using coated fuel partieles.

The test section 1S followed by a channel of constant cross sectional area to minimize upstream effects caused by discharging the working air into the laboratory room.

The size of the test section and the diameter of the spherical elements were selected from the following considerations.

In a practical configuration of a nuclear reactor cooled by helium a typical Reynolds Number based on superficial velocity

(V o ) and particle diameter (Dp ) is of about 290.

The test set-up was then designed to cover ,the range 50 to

2000. Using air as a working fluid, a range for the product VoDp is thus fixed.

4

-A heat transfer measuring technique 18 adopted (described 1n the next section) which enforces the use of one copper instru-mented sphere which contains an electric resistance for power dissipation and thermocouples for temperature measurements.

This determines a minimum value of the diameter D which is p

one order of magnitude larger than the diameter of the coated fuel partieles. The next problem is to select a sufficient number of inert spheres of equal diameter D surrounding the active one,

p

so that a nuclear reactor core containing a large number of small partieles can be simulated.

This number, on the otherhand, is limited by cost and total mass flow considerations.

Finally, the choice of table tennis balls was adopted for the inert spheres, thus giving a value of about 37 mm for the diameter D • A ratio of container width to sphere diameter of

p

15

was selected so that the square test section has dimensions mentioned above and giving a total number of 3375 spheres.

They are laid in carefully one by one to form a "dense cubic"

(or "octaedric) packed bed characterized by a void fraction of 0.26. In this arrangement half-spheres are used at the walls of the test section and one-quarter spheres in the corners. It is expected that, under these conditions, wall effects are minimized even in the presence of local obstructions.

Great care was taken to avoid the presence of a screen at the entrance of the test section supporting the packed bed.

This lS done by using metallic W1res stretched from opposite walls of the test section along which the spheres of the first lower layer of the bed are strung like beads on a string.

Figure 2-a and bare photographs of the tes~ section. Figure 2-B lS taken during the packing operation. The 1ns-trumentated sphere can be seen among the inert ones.

3. HEAT TRANSFER MEASURING TECHNIQUE

As seen in figure 1 a~r enters the test section at room tempe-rature (Tg) and flows around inert spheres which are also at or very near room temperature.

One of the spheres ~s made of copper and instrumented with an internal electric resistance, which can dissipate a maximum of about 30 watts, and thermocouples for temperature measurements.

In fact, the detailed design of the sphere ~s different as shown below whether one is interested ~n average or detailed dis-tribution of heat transfer rates.

A steady a~r flow being established thraugh the test section, a certain time (af the order of thirty minutes for average heat transfer measurements, and of more than one hour for local heat transfer measurements) is needed af ter swit~hing on the power (Q) dissipated inside the instrumented sphere, ta reach a steady

sur~ace _{temperature T s •}

Then the heat dissipated ~s exactly convected away by the coo1ant gas.

It shou1d be noted that copper was purpasely selected to manufacture the working sphere. It ensures a uniform temperature of its skin despite local surface variations of the heat transfer rate.

3.1 Measurement of average values

Figure 3 s~pws the sphere which was used for these measurements. It was machined into two parts, instrumented with thermocoax

6

-Knowing the total heat flux Q from the measured power dissi-pated inside the sphere and the driving temperature ~T=Ts-Tg.

one can calculate an "average" heat transfer coefficient h = Q/Sp.~T and Nusselt number Nu = hDp/kg, where Sp = n.D~ is the total skin area of the sphere and kg the thermal conduc-tivity of air. From the mass flow measured upstream of the settli chamber, the superficial velocity Vo is calculated thus giving

the Reynolds number Re = VoDp

v

where v is the kinematic viscosity of air.

The results of average values measurements are presented ln a dimensionless form Nu = f(Re)

3.2 Heat transfer distributions

The design of the sphere used for local measurements of the heat rate is more complex as shown by figures 4-a and b.

A small cylindrical element is thermally isolated from the rest of the sphere. lts outside looking base occupies only 1

%

of the total surface of sphere and, in that sense, provides "1 oca l"

values of the heat transfer rate.

As before, section 3-1, the sphere is heated up by inner power dissipation and its skin temperature stabilizes to a measured value T •

s

In addition, heat is supplied directly to the cylindrical element at a rate such that its outside looking face is also at temperature T s • Everything being practically at uniform tempera-ture and the cylindrical element being isolated from the rest of the sphere, this amount of heat is a direct measure of the local heat flux, which is then presented in the form : Nu

=

h Dp/kg where h 15 now based on the power dissipated in the cylindrical

eleffient and on the outside looking face of this element. Distri-bution of Nu over the surface is obtained by rotating the sphere to change the position of the copper element with respect to the upstream flow.

To simplify the test set-up, it was decided to avoid remote control of this rotation. Therefore one has to unpack the bed each time.

It was verified that this procedure did not cause any errors 1n the repeatability of the measurements.

B

-4.

PRELIMINARY MEASUREMENTS

A series of preliminary tests were made to determine a suitable value for the driving temperature ~T

=

_{T s - Tg which}

could be varied by adjusting the amount of power dissipated into the instrumented sphere.

In addition, the relative importance of var10US heat transfe mechanisms was examined.

A maximum temperature of about 100°C is fixed by the materie of the table tennis balls and the coolant gas temperature 1S

about 20°C. The driving temperature is thus limited to a maximum

of

Booc.

The preliminary tests showed that the heat transfer

coefficient was independent of ~T up to this maximum value.

Therefore a suitable value of 40 to 50°C was selected for

~T. In addition to forced convection, one has to consider three possible mechanisms for heat transfer from the instrumented spher to its surroundings.

1. Conduct ion through contact points between the heated sphere and its neighbouBs

2. Natural convection at low Reynolds numbers

3. Conduction through surrounding non negligible air, when at rest.

Tests were made to determine their relative importance. The results are summarized in figure

5.

It glves the power dissipated in the sphere which 1S needed

to maintain a given óT of about 45°C when the number of contact points between the heated sphere and the neighbouring ones is

This was done in the presence of natural convection and without simply by inserting cotton in the various gaps between the spheres. Under norm al operating conditions (12 contact points) it is seen from figure 5 that the three above mentioned machanisms contribute for 0.082, 0.105 and 0.206 cal/sec respectively.

In the presentation of the results of the final tests, all the measurements were corrected by 0.la7 cal/sec which is the sum of the two first effects.

Indeed these are specific aspects of the present technique

of heat transfer measurement and not of the actual problem of the

- 10

-5.

RESULTS

5.1 Average heat transfer

The tests were first made without loca1 obstruction.

The resu1ts agree remarkably weil with previouèly published data as shown in Figure

6.

This figure gives the measured Nusse1t number versus Reyno1ds number as defined in section 3.2.

Some of the results (for example, curves Z2, L4, L8) indi-cate lower Nusse1t numbers than the others. One reason is that in these cases, wall effects were present.

The effect of alocal obstruction was then considered. In the real situation of the nuclear reactor core, partial

obstruction of the packed bed is possible due to dust retention or breakage of some of the fuel partieles.

It did not appear pos~ible to simulate simply such a situa-tion but rather to test a certain number of configurasitua-tions in which the interestices between the working sphere and the neighbouring ones were progressively obstructed.

Examples of such obstructions by plexiglass plates are shown in figure

7.

The results are given 1n figure

8

for the various types of obstructions identified by the same numbers as those used in figure

7.

It is seen that in each case two different laws are obtained depending whether the Reynolds number is larger or smaller than 250.

In addition, the exponent B (i.e. the slope of the curves

1n figure

8)

is nearly independent of the type of obstruction.

It is also concluded that the effect of alocal obstruction may be very pronounced, inasmuch as it reduces the heat transfer by a factor which can be as high as three.

5.2 Heat transfer distribution

As the time needed to obtain steady flow conditions was large, the test program was lirnited to the three fOllowing

'situations

- heat transfer without obstruction

- heat transfer in the presence of type 5 and 6

obstruc-tions (see figure

7).

The measurements were made along a great circle of the sphere. The results are shown in figure 10 where Nu is plotted versus Re. As may be seen, large variations of local heat

transfer exist over the surface of the sphere in the ratios

1/3, 1/6. 1/8 respectively for the th ree conditions which were

- 12

-6.

CONCLUSIONS

Average and local measurements show the important influence of local obstructions on heat transfer between a sphere in the packed bed and the coolant gas.

Consequently, a uniform heat transfer is impossible if obstructions are present.

Under these conditions hot spots are expected which ~n turn aWRy may cause new ruptures and further obstructions leading to unsafe operation in a practical configu~ation.

It thus seems necessary in a practical configuration to filte the coolant gas upstream of the packed bed and decrease the proba~

bility of ruptures by a careful construction of the particles.

ACKNOWLEDGMENTS

We wish to express our appreciation to Mr. F. Thiry, technica englneer, for his advice and continuous assistance in the reali-zation of this work.

TEST FAC/L/TY

TEST SPHERE

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Teilung } Einheit \

Logar. Division 1-300 u. 1-10000 Unité I 62.5 mm Ed. Aernl-Leuch, Bern, Nr. 551

11

1

I

I I

Test sphere in the pa~kect bed

<:

a

-I-.... <...J :::, 0::: I-.... (I) Cl:)

a

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Sphere at t,he aiddle er N

b . b d U z

o Btructl.on, a eve er un er t-SPhere

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1N

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=

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- - -

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f-5

6

7

obstrllntion at the same Nu

=

1,192 ReO,b44 Nu = 0,500 ReO,703 level as spheres of the

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1 - - -

-Obstruntion of 9

interstines, sphere at Nu

=

1,380 ReO,bOO Nu

=

0,'328 ReO ,638 the middle

r-- - - -- - - - -- - - " - - - -- - - -- - - -

-Obstruntion of Hi inter- N _ 1 318 R 0,483 N"u s: 0,37'-> ReO, 723

sti~es, sphere at the middlllu - , e ...

~bstr\lntion ~

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-tion 3.

Sphere at the middle of

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t'

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Nu

Nu

=

0,282 HeO,694 B

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