FM 301 B6(b)

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FM 301

Flow of Solids through Bins

andPneumatic Conveying

Date of Experiment : 28th

September

Date of Presentation : 3rd

October

Lab Group: B-6 (b)

Rupak Kumar 09D02033 (Report)

Akshansh Gupta 09002039 (Presentation)

Sourabh Biswas 09002044 (PPT)

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PART A: Flow of solids through Bins

OBJECTIVE:

The objective of our experiment is to study the effect of the powder level above the exit and

the effect of particle diameter and orifice diameter on the mass flow rate.

MOTIVATION:

Several chemical processes involve solid raw materials or products in the form of powders

(e.g. cement manufacture, pharmaceuticals, etc). The powders need to be transported during

their processing, hence their flow properties are of considerable importance. An application,

which is very common, is the flow of powders from storage bins & hoppers, under the

influence of gravity.

THEORY:

Particulate flow consists of both liquid-like and solid like characteristics. They occupy the

volume of the container, and exert pressure on the side walls of the containers, which is liquid

like behaviour. Unlike liquids, the shearing stress is proportional to the normal load ratherthan to the rate of deformation. Like solids, they can sustain a shear stress, though the

magnitude of the shearing stress at a point is generally indeterminate.

The discharge flow rate depends mainly on the orifice geometry, the nature of the powder and

is nearly independent of the height of the powder above the exit, and the vessel diameter. If

the effect of particle diameter is ignored, then based on the dimensional analysis, the mass

flow rate is given by

Where Do is the orifice diameter, g is the acceleration due to gravity, is the bulk density of

the solids and C is constant.

Beverloo et al. (1981) have shown that the mass flow rate is given by

where d is particle diameter, k and C are constants.

By plotting W2/5

versus Do, we can check whether straight lines are obtained for the two

different particle sizes. The constants C and k can be obtained from the slopes and intercept

of the lines respectively.

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EXPERIMENTAL PROCEDURE:

Figure 1 : Flowchart showing the procedure followed in the experiment

Fix the plate havingorifice diameter as 7.9mm at the bottom of

the bin

Fill the bin with thematerials of particle size

1.1 mm size upto 300mm height in the bin

Release the cork toallow the sand to flow

out and record the timetaken till the sand stops

coming out

Weigh the sandcollected

Repeat the above 4steps for different orifice

plate

Follow the same aboveprocedure for particle

size 0.7 mm

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SCHEMATIC DIAGRAM:

Figure 2 : Schematic diagram of the apparatus

CALCULATION PROCEDURE:

Figure 3 : Calculation procedure followed

Calculate the mass flow rate

Draw the graph between W2/5 and orificediameter Do and obtain equation of lineobtained

From the slope of graph calculate the constant Cby comparing it with Beverloos equation

From the intercept and value of C calculate valueof constant k

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OBSERVATIONS:

Weight of the tub = 189 gm

Average particle diameter = 1.1 mm

Orifice

Diameter

(mm)

Height

(mm)

Mass

collected

(kg)

Actual Mass

collected (kg)

Time Taken (sec) Mean Mass

flow rate W

(gm/s)

7.9 300 2.302 2.113 241.4 8.753

7.9 200 1.608 1.419 162.77 8.717

10.8 300 2.288 2.099 94.5 22.211

10.8 200 1.598 1.409 68.16 20.671

15.8 300 2.403 2.214 36.9 60

15.8 200 1.634 1.445 35.5 40.704

20.5 300 2.332 2.143 16.21 132.202

20.5 200 1.666 1.477 11.4 129.561


Orifice

Diameter

(mm)

Height

(mm)

Mass

collected

(kg)

Actual Mass

collected (kg)

Time taken (sec) Mean Mass

flow rate W

(gm/s)

7.9 300 2.186 1.997 210.5 9.486

7.9 200 1.545 1.356 142.56 9.511

10.8 300 2.273 2.084 84.58 24.639

10.8 200 1.564 1.375 59.01 23.301

15.8 300 2.283 2.094 32.69 64.056

15.8 200 1.592 1.403 22.07 63.570

20.5 300 2.273 2.084 14.5 143.724

20.5 200 1.646 1.457 10.8 134.907

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GRAPHS:

From the above graph, slope = 0.367

Intercept = -0.54


Intercept = -0.529

y = 0.3672x - 0.54

R = 0.9984

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

Mass

flowrate^(2/5)(gm/sec)

Orifice Diameter D (mm)

W^(2/5) Vs D for grains of 1.1 mm

with Height 300 mm

Series1

Linear (Series1)

y = 0.3501x - 0.529

R = 0.9569

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

Massflowrate^(2/5)(gm/sec)


W^(2/5) Vs D for grains of 1.1 mmwith Height 200 mm

Series1

Linear (Series1)

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Intercept = -0.539


Intercept = -0.453

y = 0.3781x - 0.5397

R = 0.9974

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

Massflowrate^(2/5)(gm/sec)



Series1

Linear (Series1)

y = 0.3668x - 0.4536

R = 0.9993

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

Mass

flowrate^(2/5)(gm/sec)



Series1

Linear (Series1)

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RESULTS:

Particle size of diameter 1.1 mm Particle size of diameter 0.7 mm

Error Analysis

Standard deviation (s) = For particle size of diameter = 1.1 mm

C = 0.002 or (10.9%)

k = 0.037 or (2.69%)

For particle size of diameter = 0.7 mm

C = 0.017 or (35.27%)

k = 0.153 or (13.25%)


C = 0.0172 0.002

k = 1.3555 0.037


C = 0.0411 0.017

k = 1.0775 0.153

Height of

sand level(mm)

Value of

constant C

Value of

constant k

Height of

sand level(mm)

Value of

constant C

Value of

constant k

3000.0182 1.337

3000.0499 1.001

2000.0162 1.374

2000.0323 1.154

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CONCLUSION:

The graph between W2/5

vs Do is a straight line for both the samples of the sand and the slope

and the intercept in both the graphs are nearly equal. The Particle flow depends only on the

orifice and the particle diameter while the fluid flow depends on the height of the column and

the diameter of the orifice and the vessel. The mass flow rate is independent of height

because the stress is mostly borne by the walls of the container and the stress at the orifice is

hence independent of H. Also, the mass flow rate increases with increasing orifice diameter

and decreases with increasing particle size. Unlike liquids, the shearing stress in particulate

solids is proportional to normal load rather than the rate of deformation.

The value of constant k appearing in the Beverloos equation decrease with decrease in the

particle size. The term (DOkd) accounts for the effective diameter that is available to the

particles to exit from the vessel. Further, k signifies the resistance that is offered by the walls

of the opening of exit to the particle flow. Thus, as the particle size decrease, resistance

decreases & so does the value of k. This is proved experimentally too as we obtain lesservalue of k for diameter 0.7 mm.

SOURCES OF ERROR AND PRECAUTIONS:

While filling the sand in the bin, the container should not be shaken in order to level the sand

as it will then resemble a packed bed, and not the free flowing sand that is required for the

experiment.

The height level on top should be levelled out by filling the last 10 mm of sand by hand, sothat the height level of the sand is uniform throughout the cross section of the bin. The orifice

should be placed such that it is inclining downwards like the inner side of a funnel.

The stopwatch should be started as soon as the stop cork is taken out, and this is a source of

error that will propagate into mass flow rate calculations. Also, care should be taken that the

sand does not fall out of the container.

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PART B : Pneumatic Conveying

OBJECTIVE:

The objective is to study qualitatively the different flow regimes for different gas and solids

flow rate for horizontal pneumatic conveying and also to measure pressure drops for gas-

solid flow for different gas and solids flow rates.

MOTIVATION:

Pipeline transport of particulate solids has a number of advantages over conventional

transportation systems such as conveyor belts, the former systems are compact and require

much less maintenance. They are commonly used for in-plant transports of solids (e.g. in

cement plants) as well as for loading and unloading materials from trucks and ships (e.g. food

grains).

THEORY:

Dilute Phase Transport:

When the gas volume flow rates are much higher than that of the solids, the transport of

solids is said to be in the dilute phase. In this case there is a nearly uniform distribution of

solids across the pipe cross-section of the pipe and along its axis. In this case the pressure

drop for the flow is given by

where Pfis the pressure drop due to flow of gas alone and d is the extra pressure drop

due to the pressure of the particles. fcan easily be evaluated from friction factor charts. An

expression for calculating d is

Where, = density

u = velocity

= volume fraction of gas in the pipe and the

Subscripts f and p refer to fluid and particle respectively, L is the length of the pipe, and

m = Gp /Gfis the ratio of solid to gas mass flow rates, Cds is the drag coefficient for a single

particle moving through the fluid at a velocity (uf- up).

Dense Phase Transport:

As the air flow rate is reduced below a threshold limit, the particles start to fall out of the gas

stream, and settle to the bottom of the pipe. This decreases the actual flow area, thus

increasing the pressure drop across the pipe. Further reduction in flow rate leads to more and

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more pressure drop. This phase is known as the Dense Phase, and is undesirable for solid

transport.

The velocity at which the solid particles first begin to settle is known as the Saltation

Velocity. In designing, the saltation velocity is used as a basis for choosing the design gas

velocity in a pneumatic conveying system. Usually, the saltation gas velocity is multiplied bya factor, which is dependent on the nature of the solids, to arrive at a design gas velocity.

When the gas velocity becomes low (below the Saltation Velocity the particles settle at the

bottom of the pipe. The settled particles are transported by partly sliding along the pipe.

The distribution of solids in such cases where mass flow rate(m) is high generally non-

uniform and this results in large pressure fluctuations. An empirical correlation for the

pressure drop in dense phase transport is

Where, D is the pipe diameter and ds is the mass per unit volume of solids in the pipe.

EXPERIMENTAL PROCEDURE:

Start compressorand fill the bin with

sand

Adjust the flow rateof air to high value

Start the flow ofsand

Measure the flowrate of sand by

collecting it for a fixtime

Also meaure thepresure dropandobserve the flow

regime

Decrease the flowand repeat the

procedure

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SCHEMATIC DIAGRAM:

OBSERVATIONS:

Weight of the mug = 110 gm


Density = 2.8 gm/cc

Air

Flow(m/hr)P(mm) Mass collected

(gm)

Time taken

(sec)

Actual mass

collected

(gm)

Mass flow rate

(W) (gm/sec)

13 13 353 20.28 243 11.982

12 11 341 20.31 231 11.373

11 9 339 20.08 229 11.404

10 8 343 20.22 233 11.523

9 15 279 18.98 169 8.904

8 19 245 20.30 135 6.650

7 26 209 20.18 99 4.905

6 27 184 19.91 74 3.716

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RESULTS AND CONCLUCIONS:

The Air Mass flow rate vs Pressure drop was plotted as shown below. Initially, as the air flow

rate is very high, dilute phase is observed. There is no settling of particles at the bottom of the

pipe, and a well mixed stream of particles and air exits from the pipe.

The above graph indicates the different phases. The first decreasing part shows the dense

phase where the sand particles are accumulating in tube. The increasing part of the graph

shows the dilute phase in which there is no accumulation.

From the above graph, the optimum flow rate to minimize the pressure drop across the tube is

10 m3/hr. And the corresponding mass flow rate is 11.523 gm/s.

y = -0.005x2 - 0.2543x + 14.404

R = 0.9304

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Massflowrate(gm/sec)

P(mm of CCl4)

Mass flow rate vs Pressure difference

Series1

Poly. (Series1)

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14Pr

essuredrop(mmofCCl4

Air flow rate (m3/hr)

Pressure drop vs Air flow rate

Series1

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From graph we see that as the flow rate was decreased, the pressure drop reached a minimum

value and then started increasing. Now in the dense-phase pneumatic conveying more and

more solids settle down at the bottom of the pipe as the flow rate of air is decreased. This is

characterised by increase in pressure drop mainly due to large amount of frictional losses

between solid particles and pipe.

In the dilute phase transport, the physical forces contributing to the pressure drop are air-to-

pipe friction, air-to-particle friction and pipe-to-particle friction.In the absence of gravity, the

particles will never settle down at the bottom of the pipe. Thus, the particles will always be

uniformly distributed across the cross section of the pipe, whether the gas flow rates are low

or high.

SOURCES OF ERROR AND PRECAUTIONS:

The readings should only be taken once steady state is achieved and the pressure difference

becomes constant. Moreover, the collection of sand and starting of stop watch should be

simultaneous and the actual time should be considered while doing the calculations. The

stopping of stop watch and the removal of mug should also be simultaneous. Also, the hopper

should be continuously refilled with sand.

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APPENDIX:

Sample calculations for flow of solids through bins.

From graph 1, W2/5

= 0.367 Do - 0.54

Comparing with W = C x x g (DOkd)

5/2

= M/ (h x x d2

x ) = 1.425 gm/ cm3

We get,

(C x x g)0.4= 0.367

(C x x g)0.4

x K x d = 0.54

Solving we get, K = 0.54/(.367 * 1.1) = 1.337

C = 0.3672.5

/( x g) = 0.0182

From graph 2, W2/5

= 0.35 Do -0.529

Comparing with W = C x x g (DOkd)5/2 = M/ (h x x d2 x ) = 1.425 gm/ cm3

We get,

(C x x g).4

= 0.35

(C x x g).4

x K x d = 0.529

Solving we get, K = 0.529/(0.35 *1.1) = 1.374

C = 0.352.5

/( x g) = 0.0162

From graph 3, W

2/5

= 0.378 Do - 0.539Comparing with W = C x x g (DOkd)

5/2

= M/ (h x x d2 x ) = 1.365 gm/ cm3

We get,

(C x x g).4

= 0.378

(C x x g).4

x K x d = 0.539

Solving we get, K = 0.378/(.539 * 0.7) = 1.001

C = 0.5392.5

/( x g) = 0.0499

From graph 4, W2/5= 0.366 Do - 0.453

Comparing with W = C x x g (DOkd)5/2

= M/ (h x x d2 x ) = 1.365 gm/ cm3

We get,

(C x x g).4

= 0.366

(C x x g).4

x K x d = 0.453

Solving we get, K = 0.366/(.453 * 0.7) = 1.154

C = 0.4532.5

/( x g) = 0.0323

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FM 301 B6(b)

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