The Behaviour of L-Valves With Granular Powders

7/21/2019 The Behaviour of L-Valves With Granular Powders

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Powder Technology 67 (1991) 163-174

163

The behaviour of L-valves with granular powders

D Geldart

and

P J ones

School of Powder T echnology, Departmen of Chemical E ngineeri ng, Universiw of Bradford, Bradf ord, West Yorkshire

BD7 IDP (UK)

(Received July 19, 1990; in revised form February 4, 1991)

Abstract

An extensive experimental program was carried out on three sands, all group B powders, in L-valves

of diameter 40, 70 and 100

mm. The radius of the elbow, the number of aeration points and the

inclination of the horizontal section influence the solids flow rate. In a system in which both the feed

hopper and the discharging solids are at atmospheric pressure, the maximum solids fluxes achievable

can be calculated from hopper discharge correlations and are in the range 600- 1200 kg/(m*.s). The

minimum aeration gas requirement is determined by the incipient fluidization velocity of the powder.

Correlations are given from which the aeration gas flow rate and the pressure drop across the L-valve

can be calculated for any solids flux, and a design procedure is

given for systems using group

B

solids.

Introduction

L-valves belong to a class of devices for controlling

the flow of granular materials with injected gas alone.

These non-mechanical devices also include J- and

V-valves, and because there are no moving parts in

contact with the solids, they are therefore particularly

suitable for use in environments which are hostile

to materials of construction, such as high temper-

atures, abrasive particles and corrosive gases. They

are cheap to construct, do not seize up, and can be

easily replaced.

In this study, carried out under cold conditions,

the objectives were to study the influence of pipe

diameter and type of solids on the operability of

the L-valve system, to understand the parameters

which influence its behaviour and to devise a strategy

for design and scale-up.

Equipment

The basic solids circulation system is shown in

Fig. 1. It consists of a mechanical conveyor, a large

hopper, an L-valve and an inclined chute. Both the

top of the feed hopper and the discharge end of

the L-valve are vented to atmosphere. The tubular

chute, of diameter 150 mm, is inclined downwards

to give free flow of solids into the elevator feed

hopper and has a segment cut out of its upper surface

half way down its length. Rotation of the chute

AERO-MECHANICAL

ELEVATOR

AIR-SLIDE

Fig. 1. Solids circulating system.

through 180 on its axis allows the solids to be

diverted into a container for a time, so that mass

flow rates of the solids can be measured. Some early

experiments were done using an air slide instead of

the chute.

0032-5910/91/ 3.50 0 1991 - Elsevier Sequoia, Lausanne


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164

The arrangement of the various L-valves is shown

in Fig. 2. The aeration point (AP) is in every

case

50

or 100 mm above the centre line of the horizontal

section. The pressure tappings contain a small wad

of cotton wool to prevent ingress of particles and

are connected to water manometers by rubber tubing.

In most cases, there are four tappings around the

circumference at each of the lower levels. With one

exception, all the L-valves are made of Perspex to

permit visual observation of the flow. The pipes are

40, 70 and 100 mm internal diameter, have 555mm

long horizontal sections and 3..52- or 3.81-m long

vertical standpipes. In addition, two 40-mm internal

diameter steel pipes were used, one being fitted with

a flexible elbow to allow the horizontal section to

be inclined downwards at various angles. A limited

number of tests was carried out in which a 280-mm

long horizontal section of 20-mm bore Perspex tube

replaced the same length of 40-mm bore pipe, thus

providing a constriction in the discharge end of the

L-valve.

The feed hopper consists of a 600-mm diameter

cylinder with a lower conical section having a half-

angle of 30. For the powders used, this acted as a

mass flow hopper. Smaller conical sections could be

40mm

40mm

c

5s

Steel L-Vdv. wtth

bolted to the bottom flange of the main cone to

match up with the different sizes of downcomer.

This general arrangement has several advantages

over the more usual method involving return of solids

to the feed hopper by pneumatic conveying.

- Solids mass flow rates can be measured directly,

eliminating the need to use calibrations or mea-

surement of particle velocities at the wall, both of

which can be unreliable.

- The pressure balance around the loop depends

only on the L-valve operation and not on pressure

drops in the return loop.

- Attrition of the solids is negligible.

Solids used

The full experimental programme involved four

sands, vermiculite, and a fine coal char. However,

the behaviour of the group A powders (one of the

sands, the vermiculite and the char) wasvery different

from that of the group B solids and will be discussed

in a separate paper. The properties of the three

sands discussed in this paper are summarized in

Table 1.

The mean sieve sizes are calculated from

-Q

%

s

49

%

-a 2

Q i

-AP o-

p,

---- -

-

70 and 1OOmm

Perspex L-valves

::

h

1

43

/

0

L-Valva with Fixad 9OElbow

Flexlbl. Elbow Dbn nmlons In mm

Fig. 2. Dimensions and positions of pressure tappings in 40-, 70- and loo-mm diameter valves.


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16.5

TABLE 1. Properties of the powders used

Property

Sands

Sl s3 s4

Mean sieve size ci, (pm) 280 500 790

Surface-volume diameter 2, (em) 243 435 650

Particle density pr (kg/m3)

2645 2604 2661

Bulk densities:

Loosely packed paLp (kg/m3) 1562 1.527 1534

Tapped IJ~T (kg/m3)

1668 1685 1687

Voidages:

LP

0.409 0.413 0.423

Q

0.369 0.353 0.366

Minimum fluidization

velocity U,, (cm/s)

6.4 20.4 40

1

dp= -

P

and the mean surface-volume diameter 8, was ob-

tained by measuring

the

pressure drop across a fixed

bed of the powder and back-calculating d,, using

the Ergun equation. The minimum fluidization ve-

locities U,r and the tapped and loosely packed

bed

voidages were also separately measured.

Experimental procedure

After filling the system with the chosen solids, the

aeration gas flow rate was set at a value which gave

a high solids circulation rate, and the rig was run

for a few minutes. It was then shut down and restarted

at a low air flow so that solids just began to trickle

from the discharge. Invariably, after a short time,

the solids flow stopped and the air had to be increased

until a condition of minimum continuous discharge

prevailed. The solids flow rate was measured five

times and an average taken, the air flow rate noted,

and the pressures up the standpipe recorded. The

aeration rate was increased by stages until a maximum

was reached. No hysteresis was observed on de-

creasing the air flow. In the 40- and 70-mm diameter

pipes, the maximum mass flow was heralded by the

disappearance of the moving bed in the upper part

of the standpipe, and its replacement with streaming

solids flow. In the lOO-mm diameter valves, the

maximum was limited by the capacity of the me-

chanical conveyor, which was about 3 kg/s. Another

constraint on the solids flow rate was that with the

coarsest sand, in the 70- and lOO-mm diameter pipes,

sonic velocity was reached in a single aeration nozzle,

thus limiting the air flow. Because it was not prac-

ticable to increase the diameter of the nozzle, we

used three nozzles at the same level.

Results

General observations

On

the whole, our visual observations agree with

those made in the pioneering work of Knowlton and

Hirsan [l] and are illustrated in Fig. 3. At very low

flow rates (Fig. 3(a)), there is a narrow, fast-moving

stream of solids at the top of the horizontal pipe

and virtually no movement detectable in the stand-

pipe. The width of the channel increases as the size

of the sand in the rig is increased. However, there

is significant segregation by size in the horizontal

section, with the smallest particles in the size dis-

tribution predominating at the top of the pipe.

At medium solids flows, dunes or ripples move

across the top of the pipe at a frequency of about

4 per second and cause fluctuations both in the

solids discharge rate and also in the pressures mea-

sured just above the aeration position.

At high solids rates, the dune frequency falls to

about 1 per second. When the maximum solids flow

is reached, accompanied by streaming and flow fluc-

tuations, any further increase in gas injection causes

a sharp reduction in solids flow. Knowlton and Hirsan

[l] attributed this to the fluidization which occurred

in their downcomer when the pressure gradient in

la)

LOW

AERATI ON

RATE

l b)

MEDI UM

AERATI ON

RATE

ICI

HIGH

AERATI ON

RATE

Fig. 3. Mode of solids discharge from L-valves.


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66

it reached bMF*g. These large pressure gradients

could occur in their rig because the L-valves dis-

charged into a vertical pneumatic conveying line

across which the pressure drop increased with the

solids discharge rate.

In our rig, the discharge end of the L-valves was

always at atmospheric pressure and we believe that,

under these circumstances, it is the size of the hopper

outlet which limits the solids discharge rate. If the

L-valve delivers a greater solids flow to the discharge

end than is fed to it by the hopper outlet, the

standpipe starts to empty and a bed level appears

at the top of the standpipe and moves downwards

with streaming solids above it. The resistance to gas

flow above the aeration point is reduced and some

of the aeration gas passes up the standpipe, leaving

less available to transport the solids through the

horizontal section and causing the discharge rate to

fall momentarily. The level, and the resistance to

flow above the aeration point, then increase, and

more injection gas passes downwards. Thus, the

system starts to operate like an automatic L-valve

[2], but with flow instability. Further increase in

aeration gas flow then starts to choke off the flow

from the hopper outlet (injecting air just below a

hopper outlet has been used successfully as a method

of controlling solids egress [3]).

To check the validity of this hypothesis, we cal-

culated the maximum flow rates out of a hopper

using the Carleton [4] equation.

g=

4V. sin p + 15p1cL2/3VS4B

D ,a;~

where

V, =

4MJ(peLprrD2).

The results are shown in Table 2A together with

the maximum fluxes achieved in the various L-valves

using the three sands. In addition, a separate test

was carried out in which the 40-mm diameter down-

comer was removed and the flow rate of sand Sl

measured as it flowed freely out of the hopper. It

can be seen that where comparisons are possible,

the maximum L-valve throughput is between 84 and

97 of the maximum flows predicted by the Carleton

equation.

In Table 2B, the highest solids fluxes quoted in

Knowlton and Hirsans paper for four different valve

sizes are compared with values calculated from

Carletons equation. Their equipment layout diagram

shows a ball valve of unspecified diameter below the

hopper outlet, and this may have reduced the max-

imum solids flux attainable; with the exception of

the 6-in valve, the maximum solids fluxes attained

were between 47 and 80 of the predicted values.

There are, therefore, reasonable grounds for be-

lieving that when the L-valve discharges at atmos-

pheric pressure the maximum solids flux capable of

passing through it is determined by the size of the

hopper outlet, or of any other restricting orifice,

such as a ball or slide valve, below it.

If, however, the L-valve has to feed against an

appreciable back pressure, such as a fluidized bed

or a pneumatic conveying line, a lower maximum

operating flux will be reached when the pressure

gradient in the downcomer approaches that of the

fluidized solids.

Effect of L-valve geometry

Elbow construction

In all fluid-particle operations, visual observation

is very helpful in bringing about an understanding

of the hydrodynamics, and it is for this reason that

most of our L-valves are made of Perspex. The

method of construction used, two tubes cut at 45

and cemented together, resulted in sharp 90 elbows.

In commercial applications, equipment has to be

made of steel, or some other robust material, and

the elbow may not be sharp, especially if the pipes

are lined with insulating bricks or cement. We there-

fore replaced the entire 40-mm diameter Perspex

system by 40-mm diameter smooth-walled steel tubing

and used a standard small-radius cast iron 90 elbow

to connect the standpipe to the horizontal section.

Because we also wanted to investigate the effect of

using a sloping horizontal section, we subsequently

replaced the cast elbow by a piece of wire-reinforced

flexible plastic pipe which, in effect, gave a large

radius elbow.

As shown in Fig. 4 for the 90 elbows (curves 1,

2, 3) at a given aeration rate, the solids discharge

rate increases as the elbow geometry changes from

sharp to gradual. Conversely, slightly less gas is

required to transport the same solids rate when the

bend is gradual. The gradual bend also improved

sensitivity of control near the minimum discharge

rate condition. It was observed that at high solids

discharge rates, considerable electrostatic charging

occurred when using the Perspex L-valves. However,

it seems unlikely that this was the cause of the

difference between the sharp (Perspex) bend and

the more gradual (steel) bends, since the biggest

differences in solids flow occurred when the elec-

trostatics were least evident.

I ncli ned elbows

Sloping the horizontal section downwards (curves

4, 5 and 6 in Fig. 4) increases the solids flow rate

at any given aeration rate and gives greater flow

stability and control at low discharge rates. However,

both with the 280-pm (Fig. 4) and the SOO-pm sand

(Fig. S), at an angle of 106, flow becomes uncon-


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167

TABLE 2. Comparison of maximum solids flow rate from Gvalves with maximum flow rate from a hopper calculated

using Carletons equation

A This work

Diameter of L-valve (mm)

40

70

100

Mean sieve size of sand (pm) 280 500 790 280 500 790 280 500 790

Max. solids flux from

637

637 - 706 792

> 792 > 381

L-valve (measured)

=3 kg/s

kg/(m* .s)

Maximum flow out Predicted

(eqn. (2)) 652

660 676 839 86.5

899 980 1026 1069

of hopper

Measured

780 _ _ _ _ _ _

- -

kg/(m.s)

Limited by capacity of conveyor.

B Knowllon and Hirsan [l]

Diameter of L-valve (in)

Mean sieve size of powder (pm)

Largest solids flux from

Lvalve quoted in paper

kg/(m* .

s)

Maximum flow out of

hopper predicted by

Carleton equation

kg/(m* .s>

1.5

2 3

6 3

260-pm sand

188~pm siderite

354

324 553

196 875

595

684 833

1071 1100

250

250

500

500

1000

Aeration rate (cms/sl

Aeration rate (cm 3/s1

Fig. 4. Discharge rates of 280-pm sand from 40-mm L-

valves with various elbow configurations.

Fig. 5. Discharge rates of 500~pm sand from 40-mm steel

L-valve with various elbow configurations and one aeration

point.

trollable at about two-thirds of the maximum solids

flow rate and no further increase is possible. The

angles of repose of unaerated sands are shown on

Fig. 6, but in practice the angles of partly-aerated

Elbow angle

0 goo

e g4o

sands will be lower. This, and visual observation,

leads us to believe that the inability of the 106 valve

to deliver the maximum solids rate is caused by

extensive bypassing of gas along the top of the tube.


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168

500~m5ANO [----I ,4.26

GLE OF REWSE

DI AGRAM : A B C 0

ELBOWANGLE : 90 94 98 106

Fig. 6. Fraction of L-valve discharge section occupied by solids at various elbow angles.

Constr ucti on of horizontal secti on

In a limited number of tests using sand Sl, the

final 280 mm of the horizontal section of the 40-

mm diameter Perspex L-valve was replaced by an

equal length of 20-mm diameter tube positioned

concentrically. The effect is shown in Fig. 7. The

ability to control finely the solids flow rate was much

improved, particularly at low aeration rates. Thus,

a steady minimum discharge of 6 g/s was possible

with the constriction in place compared with 35

g/s in the basic valve. However, the maximum dis-

charge rate achievable was much reduced. In contrast,

Knowlton and Hirsan [l] reduced the diameter of

Wlthout constriction

q With constriction

to 20 mm I . D.

1

\

p \

I

I

L

/

Aeration rate Icm3/d

Fig. 7. Discharge rates of 280-pm sand from 40-mm Perspex

Lvalve showing effect of constriction on horizontal section.

their entire horizontal section and found that it had

little effect upon the discharge rate for a given

aeration rate.

Number of aerati on point s

Most of the experiments were done using only

one aeration point positioned on the outside of the

elbow. However, when using coarse sand S3 in the

larger valves, high air flow rates were required, and

sonic velocity was approached in the injection nozzle.

Since the supply pressure was limited to 5 bar, this

restricted the air flow rate to less than about 1.5

l/s. With the thin-walled Perspex standpipes, it was

not practicable to use larger nozzles, so we resorted

to splitting the air supply between three injection

nozzles with that on the inside of the elbow not

being used. Some of the results are shown in Fig.

8. Because of the sonic velocity limitation described

above, as expected, higher maximum air and solids

rates were achieved with three nozzles than with

Fig. 8. Discharge rates of 280-,

500- and 790-pm sand

from 70-mm

L-valve showing effect of number of aeration

points.


7/12

169

only one. What is surprising though is that at any

given aeration rate the solids rates were somewhat

lower when using three aeration points. It is con-

jectured that the air from the two nozzles at 90 to

the single nozzle was bypassing the inside of the

elbow. Thus, although all the injected air is used in

dense phase transport in the horizontal section, much

less is available to assist solids flow at the inside of

the elbow.

Effect of pi pe diamet er and part i cle si ze

Knowlton and Hirsan [l] noted that more aeration

gas is required to achieve a given solid flow rate as

particle size and pipe diameter increase. This is

confirmed by our data shown in Figs. 8 and 9,

respectively. As Knowlton [2] pointed out, the total

gas flow through the valve, Qt, is larger than that

injected because in almost all cases a gas flow, Q,,,

is entrained downwards in the void spaces between

the particles so that

Qt =

QDC Qeti

(3)

Knowlton and Hirsan [l] showed how Qnc may be

calculated from the pressure gradient in the down-

comer, and we shall address that question later in

the paper. Until now, however, there has been no

way of correlating Qext with solids flow rate.

The data for the 280-pm sand are replotted in

Fig. 10 as solids mass flux G, versus the superficial

velocity V,, of the aeration gas. The form of the

4000

3000

z

2

0

E

I

; 2000

f

.E

=

P

3

1000

0

00 0

Aeration rate cm3/s1

Fig. 9. Discharge rate of 280-wrn sand VS. aeration rate

for 40-, 70- and lOO-mm Perspex L-valves with one aeration

point.

1000 -

800 -

70mm 9

Uert

km/s)

Fig. 10. Solids discharge flux for 280-pm sand vs. aeration

rate expressed as superficial gas velocity in the L-valve.

curves in Fig. 10 suggested that the data might lie

on one curve if

GJD

were plotted instead of G,

and, indeed, the use of

GJD

for the correlation of

both dilute and dense phase pneumatic conveying

data has a sound theoretical basis [5]. When data

for the other sizes of sands were plotted in this way,

it was noticed that the minimum superficial aeration

velocities were similar to the minimum fluidization

velocities for the respective sands, and this gave the

idea of plotting GJD against U,,lU,,,,. The results

are shown on Fig. 11 for all the sharp 90 elbows.

The least-squares fitted equation is

GS

- =3354+ -2965

D

(4)

mf

The results of Knowlton and Hirsan [l] were not

included in calculating the correlation, but they are

shown on Fig. 12 compared with eqn. (4). Apart

from the data for their finest sand, the agreement

is quite good. It follows from earlier comments that

eqn. (4) gives minimum values for

G,/D

since having

elbows rounded at the inside, or horizontal sections

which slope downwards, give higher discharge rates

for a given aeration rate.

Pressure pr ofi l es and gas J?OW n t he downcomer

The maximum pressure in the rig occurs at the

aeration point, and for all three sands it decreases

linearly with increasing vertical height (Fig. 13).

Because the profiles are linear, the pressure gradients

can be calculated and cross-plotted against aeration


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170

V?llW

Symbol

1

2 3 4 5

6

hxt /bF

Fig. 11.

G lD vs. U llJ

for sharp 90 elbows - this

work.

is

E

r

y

5000

e

d

0

4

Aeration

0

0

500 1000

Pressure fmmWGl

Fig. 13. Pressure profiles with 280-pm sand in 40-mm

diameter Perspex L-valve (one aeration point).

.260 jlnl

sand

.

188 urn slderlte

.

. /

H Equation 4

.

/

.

.

/_, , , ,

0

1

2 3 4 5 6

7

Uext h4F

Fig. 12.

G D vs. Ue lUMF

Knowlton and Hirsan [l] data

compared with eqn. (4).

rate, thus permitting a convenient summary of most

of the data on two graphs (Figs. 14, 15). It should

be noted that even at the maximum aeration rates,

which, on the 40- and 70-mm diameter valves cor-

respond to the maximum solids rates permitted by

the hopper outlet, the maximum pressure gradients

are generally below 2 000 N/m2 per metre. This

should be compared with the values which would

be achieved if the downcomer were to be fluidized,

and which can be calculated from

= / MFg = f LPg

\ J-DC

jrnt

s

c 1500

t

i;

E

P

8

.r

1000

2

5

2

m

?

3

0

500

0

0

500

1000

Aeration rate km3/sI

Fig. 14. Pressure gradients VS. aeration rates for 280~pm

sand in Perspex L-valves of various diameters.

Assuming &MF is equal to the loosely packed densities

of 1562 and 1527 kg/m3 for the 280- and 500-pm

sands, respectively, the fluidized bed pressure gra-

dients would be 15 323 and 14 980 N/m2 per metre,


9/12

171

where

v,= G,

PBLP

3000

1

7

.+

E

40 mm Isteel. 900)

\

D

t

70 mm

f 2000

8

5

G

0

.E

f

100 mm

E

4 1000

2

a

f

v

IO1 , , )

0

1000

2000

3000

Aeration rate Icm3/s)

Fig. 15. Pressure gradients vs. aeration rates for SO&pm

sand in Gvalves of various diameters.

respectively, factors of about 7 higher than the highest

values measured. Clearly then, the solids are far

from being in a fluidized condition in the downcomer

even at the highest solids rate.

At first sight, the form of the pressure profiles

seems to imply that there is a flow of gas up the

downcomer. However, as shown by Knowlton [2], a

decrease in pressure from bottom to top of the

downcomer will also be obtained if the velocity of

the gas

relat ive to

the particles (often called the slip

velocity) is upwards. In the general case, the relative

velocity between gas and particles is

v,=

. h

ELP

(6)

(7)

and lJ, is the superficial velocity of gas in the standpipe

relative to the wall.

Consider case (a) in Fig. 16, in which the downward

direction is positive; because there is a net flow of

gas upwards relative to the wall (-

V),

to an observer

travelling with the particles the gas velocity relative

to the particles

Iv,1 K - (- V,)

(8)

=v,+vs

In case (b), the gas is travelling downwards relative

to the wall (in the same direction as the particles)

at a velocity

V,,

but because it is moving more slowly

than the particles, its velocity relative to an observer

+

I-IV, Down is

the positive

direction

_i

---

I

j

l+ Vs

t

--I-

t

i

IV,1

WV.

-_ --

(b)

Fig. 16. Relative gas velocities in a downcomer. (a) Gas

travels upwards relative to wall; (b) gas travels downwards

relative to wall.

on the particles is again upwards and is given by

lKl=K-v,

(9)

In both the cases shown, because the gas is moving

upwards relative to the particles, the pressure de-

creases from bottom to top, and may be calculated

from the Ergun equation. It should be noted that

IV ,1

s an interstitial velocity, whereas the Ergun

equation is normally written in terms of the superficial

velocity U,, where V, = U ,/E. Written in terms of V,,

and assuming that the voidage in the downcomer is

equal to the loosely packed voidage eLp, we have

If we know the pressure gradient AP LDC, I V ,1 an

be calculated from eqn. (10). If AP decreases from

bottom to top, then the gas is moving upwards relative

to the particles. However, the absolute direction and

magnitude of the gas (relative to the wall) must be

found by calculating V, from eqn. (6) and inserting

it in eqn. (ll), which is obtained by rearranging eqn.

(5),

i .e.,

vg=K- lK l 11)

If V, is negative, then some of the aeration gas

passes upwards from the aeration position whilst the

rest moves downwards through the valve. If

V,

is

positive, then all the aeration gas, Q_.., passes down-

wards together with a flow Qno entrained by the

solids, where

QDC = Vd ELP

12)

Absolute interstitial gas velocities

V,

have been cal-

culated for the 280-pm and 790-pm sands using

experimental data and are shown on Fig. 17. For

the 280-pm sand the procedure was as follows:

- From Fig. 14, find the aeration rate Q,, cor-

responding to a chosen pressure gradient

AP,,,IL,, .


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172

5

B

10 -

1

5 -

Fig. 17. Gas

and particle velocities in 70-mm diameter

downcomer for

280~pm and 790~pm sands.

- From Fig. 8, find the solids mass flow rate

corresponding to this value of Qea and express it

as a mass flux G,.

- Use eqn. (6) to calculate V,, which is always

positive.

- Insert

APDclLDc

into eqn. (10) and calculate IV,].

- Calculate VP from eqn. (11). If V, is positive, the

net flow of gas above the aeration point in the

downcomer is in the same direction as the solids,

i.e.

downwards and appears on Fig. 17 below the

x-axis. Conversely, if V, is negative, then, relative to

the wall, gas is travelling upwards.

As Fig. 17 shows, there are critical fluxes G,r and

Gsz above which gas is carried downwards from the

hopper. The influence of particle size is quite marked:

for the smaller sand, G,r =20 kg/(m.s) and for the

larger GsZ.= 165 kg/(m.s). At a flux of 340 kg/(m*.s),

the gas entrained by the 280-pm sand constitutes

46 of the external aeration air, whilst in the 790-

pm sand it is less than 3 . In order to confirm that

the gas flow directions were indeed as calculated in

Fig. 17, it was decided to inject CO2 as a tracer gas

into the 280-pm sand (i) at the top of the downcomer

and (ii) mixed with the aeration gas at the bottom.

The experimental set up and details of the tests are

described in detail elsewhere [6]. Briefly, a cylinder

of pure CO2 was used to provide an injection mixture

of 4 000 ppm CO2 in compressed air. Initially, the

CO2 was injected through pressure tapping 7 (see

Fig, 2) situated flush with the wall, and gas samples

were taken at various heights and peripheral positions

around the tube. However, it was found that at high

solids flows the CO2 did not disperse radially, since

none was detected at the opposite wall, even at the

bottom of the downcomer. Subsequently, when in-

jecting CO2 at the top, an injection tube was inserted

to a position beyond the pipe centre line, and good

radial dispersion was achieved. When CO2 was in-

jected at the top of the downcomer and samples

taken at position 1, CO2 concentrations above back-

ground were undetectable up to 13 kg/(m**s), but

were -3 500 ppm at 26 kg/(m*.s) and higher. Con-

versely, when injecting CO2 at the aeration point

and sampling at position 4, CO2 concentrations were

-4 000 ppm when the solids fluxes were less than

13 kg/(m**s) or higher. Thus, the experiments were

broadly in agreement with the predicted critical flux

value of 20 kg/(m*.s).

Correlation of pressure drop

The data for pressure drops AP, between the

aeration point and the solids discharge were com-

pared with the Wen and Simons [7] correlation.

However, because their predicted values were much

too low, we correlated our data against valve diameter,

mean sieve size and mass flux of the solids. The

densities of the sands were so similar that inclusion

of 4 in the correlation could not be justified. The

best fit was obtained from

216G . 1

2 (N/m3) = s Y

~0. 63 d 0. 15

P

(13)

where LN is the length of the horizontal section of

the valve measured from the injection point in the

downcomer. However,

LH

was not varied, so all our

data refer to a length of 0.55 m.

Knowlton and Hirsans [l] data are of limited use

for comparative purposes, because they are expressed

in terms of pressure drop per unit length of down-

comer, and the system included a vertical lift line

followed by a bend and a horizontal pipe section

in addition to the horizontal L-valve section. Thus,

the pressure gradient in the downcomer in their

system would change not only in response to changes

in A? across the L-valve elbow and horizontal section,

but also because of changes in AP across the lift

line and upper bend. Nevertheless, the qualitative

dependencies of eqn. (13) are in agreement with

their work, which found that the effects on APu of

mass flux and particle size were small and propor-

tional to (G&J, where m is small.

Design procedure

We are now in a position to set out a stepwise

procedure for the design of an L-valve for any

particular configuration, mass flow rate and group

B solid.


11/12

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Identify the mean sieve size and particle density

of the solids to be controlled. Check that they

belong to Geldarts Group B 181.

Specify the maximum mass flow rate to be

controlled by the L-valve, M, ,,,=, and the hor-

izontal length of the valve,

LH.

Calculate from eqn. (2) the size of the outlet

D

from the storage hopper situated at the top

of the downcomer using a value of M, = 2M, ,,,-.

Calculate the minimum controllable solids mass

flow rate from eqn. (4) using U&J,,= 1. If this

is too high, consider sloping the horizontal section

of the value downwards to 5. Alternatively,

recalculate D in step 3 using MS= lSM, ,,.,=.

Calculate Umr for the solids at the prevailing

conditions of temperature and pressure in the

L-valve using, for example, the Wen-Yu equation

(see Geldart [9]).

Using D calculated in steps 3 and 4, calculate

the maximum operating mass flux G, ,,,=, and

from eqn. (4) calculate the maximum value of

u .

TlZ maximum volumetric flow of aeration gas

is

Q,, = U,, rrD=/4.

From eqn. (13), calculate APH.

Taking into account the system as a whole,

calculate the absolute pressure at the end of

the horizontal section of the L-valve, PL.

Calculate or specify the absolute pressure at the

top of the downcomer, Pr The pressure drop

which needs to be generated across the down-

comer is then

PL+APH-PT=APDc

(14)

If there is restricted height available such that

LDc

is virtually specified, calculate the pressure

gradient and check that

@DC

-


12/12

174

Q

DC

Q exf

Qt

u cxt

volumetric flow rate of gas in downcomer,

m3/s

volumetric flow rate of injected aeration gas,

m3/s

total flow rate of gas leaving L-valve, m3/s

superficial velocity of injected aeration gas

based on diameter of horizontal section,

m/s

minimum fluidization velocity of powder

transported, m/s

superficial velocity of gas in downcomer,

m/s

absolute velocity of gas in downcomer,

m/s

numerical value of relative velocity between

gas and particles in downcomer, m/s

absolute velocity of particles in downcomer,

m/s

weight fraction of particles having a size dpi

Greek symbols

P

half-angle of hopper cone section

@DC

pressure drop between aeration point and

top of downcomer, N/m2

AH

pressure drop between aeration point and

end of horizontal section of L-valve, N/m2

ELP

EL

P

PBMF

PSLP

4

voidage of loosely packed bed of powder,

-

gas viscosity, N

-

s/m*

density of gas surrounding particles, kg/m3

bulk density of powder at minimum flui-

dization conditions, kg/m3

bulk density of powder in loosely packed

condition, kg/m3

particle density (including all open and

closed pores), kg/m3

References

1 T. M. Knowlton and I. Hirsan,

Hydrocarbon Proc., 57

(1978)

149.

2 T. M. Knowlton, in D. Geldart (ed.), Gas Fluidizution

Technology, Wiley, Chichester, 1986, p. 406.

3 Y. Yuasa and H. Kuno,

Powder Technol., 6 (1972) 97.

4

A. J. Carleton,

Powder Techno/., 6 (1972)

91.

5 D. Geldart and S. J. Ling, Powder TechnoL, 62 (1990)

241.

6

P. Jones, M.

Phil . Di ssertati on,

Univ. Bradford (1988).

7 C. Y. Wen and H. P. Simons, AIChE J., 5 (1959) 263.

8 D. Geldart, Powder Technol ., 7 (1973) 285.

9 D. Geldart, in D. Geldart (ed.), Gas Fluidimtion Tech-

nology,

Wiley, Chichester, 1986, p. 24.

Documents

The Behaviour of L-Valves With Granular Powders