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FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT by John T. Kelley, Sr. A Research Report Presented to the Graduate Committee of Lehigh University in Candidacy for the Degree of Master of Science in Civil Engineering Lehigh University 1977

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Page 1: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT

by

John T. Kelley, Sr.

A Research Report

Presented to the Graduate Committee

of Lehigh University

in Candidacy for the Degree of

Master of Science

in

Civil Engineering

Lehigh University

1977

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. .. . ~

ACKNOWLEDGEMENTS

This study was supported principally by the United States

Army. Partial funding was also obtained for materials and computer

authorization by the Pennsylvania Science and Engineering Foundation.

The author wishes to express gratitude to Dr. Willard A.

Murray for his guidance and assistance during the research project

and in preparation of the final report.

Also to be acknowledged is Mr. E. G. Dittbrenner for his

technical expertise in the construction of the experimental apparatus •

iii

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-•

... . ...

1.

TABLE OF CONTENTS

ABSTRACT

INTRODUCTION

1.1 Theory of Fluidization

1.2 Sediment Transport using Fluidization -Proposed Applications

1.3 Approach

1

2

6

10

16

2. THEORETICAL ANALYSIS 20

2.1 Pressure in the Unfluidized State

2 .1.1 2 .1.2

Analytical Model Numerical Model

2.2 Pressure in the Fluidized State

2.3 Results of Analysis

22

23 26

27

32

3. EXPERIMENTAL INVESTIGATION 42

3.1 Apparatus

3.2 Test Procedure

3.3 Experimental Data

3.4 Additional Experimental Tests

42

48

50

50

4. DISCUSSION OF EXPERIMENTAL AND ANALYTICAL RESULTS 60

4.1 Comparison of Experimental and Analytical Flow Rate 60

4.2 Variation of Pressure with Flow Rate 61

4.3 Conditions at Incipient Fluidization 77

4.4 Distribution of Pressure· in the Media 78

4:5 Comparison of Fluidized Channels 84

5. SUMMARY AND CONCLUSIONS 87

APPENDIX A - CONSTRUCTION DRA\HNGS 91

APPENDIX B - ANALYSIS OF SNAD USED IN MODEL 94

BIBLIOGRAPHY 98

VITA 100

iv

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LIST OF TABLES .,, ..

Table Page ---

r 1 Experimental Data Distributor No. 1 51

2 Experimental Data - Distributor No. 2 52 -..

3 Experimental Data - Distributor No. 3 . 53

4 Experimental Data - Distributor No. 5 54

5 Summary of Experimental Data 55

... • f

v

I __ ..

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...

Figure

1

2

LIST OF FIGURES

Fluidization Applied to Sediment Transport

Cross Section of Fluidized Channel

3

5

3 Variation of Pressure and Bed Length for Fluidized Beds 7

4 Perspex Model used by Hagyard et al. (5 ) 12

5 Crater-Sink Sand Transport System(]) 15

6 Duct-Flow Fluidization 17

7 Seepage Analysis Flow Situation 21

8 Muskat Analysis of Fluidizing System for Unbounded Flow 24

9 Node Configuration for Finite Element Analysis 28

10 Force Balance to Determine Fluidizing Pressure 30

11 Theoretical Pressure Distribution - Dist. 1 33

12 Theoretical Pressure Distribution - Dist. 2

13 Theoretical Pressure Distribution - Dist. 3

14 Theoretical Pressure Distribution - Dist. 5

15a Fluidized Zones Predicted by Muskat Equation

15b Fluidized Zones Predicted by Numerical Model

16 Experimental Apparatus

17 Locations and Detail of Pressure Taps

18 Distributor Configurations

19a Experimental Results - Visual Studies

19b Experimental Results - Visual Studies

20a Experimental Pressure Variation at Point 1

20b Experimental Pressure Variation at Point 2

20c Experimental Pressure Variation at Point 3

vi

34

35

36

40

41

43

45

47

57

58

62

63

64

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Figure Page ......

20d Experimental Pressure Variation at Point 4 65

r 20e Experimental Pressure Variation at Point 5 66

20f Experimental Pressure Variation at Point 6 67

20g Experimental Pressure Variation at Point 7 68

20h Experimental Pressure Variation at Point 8 69

20i Experimental Pressure Variation at Point 9 70

20j Experimental Pressure Variation at Point 10 71

20k Experimental Pressure Variation at Point 11 72

201 Experimental Pressure Variation at Point 12 73

20m Experimental Pressure Variation at Point 13 74

2la Comparison of Experimental and Numerical Pressure 80 Distributor 1

2lb Comparison of Experimental and Numerical Pressure 81 .; Distributor 2

2lc Comparison of Experimental and Numerical Pressure 82 Distributor 3

2ld Comparison of Experimental and Numerical Pressure 83 Distributor 5

22 Comparison of Experimental and Numerical Fluidized Zones 85

' ..

. ,,

vii

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LIST OF SYHBOLS AND ABBREVIATIONS

A = area, square inches

d depth of burial, inches

e = porosity

F = force in y-direction y

h = head, inches of H2

0

K = hydraulic conductivity, centimeters per second

t = length, inches

tn = natural logarithm

M = strength of source or sink

P,p = pressure, pounds per square inch

P* = pressure including hydrostatic forces

P = pressure force

Pmf = minimum fluidizing pressure, inches of H2

0

Q = discharge, cubic centimeters per second

q = discharge per unit width

Qmf minimQm fluidizing discharge, cubic centimeters per second

r1,r2 radius, inches

Vmf = minimum fluidizing velocity, centimeters per second

W = weight

ys,yw = specific weight

e1,e

2 = angle from well to point

-. ~ = potential

' .. ~ = streamline flow

~ = differential operation

viii

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' •

. ..

. -.

..

ABSTRACT

Sediment can be transported using fluidization techniques by

injecting water into a channel bed via a buried fluidizing pipe having

outlet orifices. The cross-sectional shape of the resulting fluidized

channel is found to be dependent on the location of the outlet ori-

fices on the fluidizing pipe. Two analytical models are developed to

predict the fluidized channel shape for given system parameters;

discharge through the section, depth of burial of the fluidizing pipe,

and location of the outlet orifices on the pipe.

Experimentally, an optimQ~ fluidizing pipe configuration is

found to have the outlet orifices horizontally opposed. This confi-

guration yields the widest fluidized channel of five configurations

tested. Analysis indicates, however, that the fluidized channel width

results from both direct fluidization and erosion effects. Presently,

the erosion effects are not included in the analytical prediction

and are responsible for non-agreement between analysis and experi-

ments.

Experimental and analytical results show good agreement when

comparing conditions of pressure in the media as a function of flow

rate, up to and including incipient fluidization conditions .

1

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1. INTRODUCTION

Channel deterioration can be caused by stream bank erosion or

deposition of the stream's sediment load. The result in either case

is an accretion of sediment on the channel bottom causing a reduction

of channel depth. Eventually the channel deteriorates to the point

where it is no longer useful for navigation.

This deterioration may take years to occur in some cases or

it may be an annual occurrance in others. Small tidal inlets and

harbors are areas representative of the latter case. Subjected to

littoral drift and sediment from storm erosion, these channels may

deteriorate rapidly.

It has been proposed by Hagyard et al. (S) that unwanted sediment

can be removed by using a fluidization technique. Figure 1 shows both

a longitudinal and a cross-sectional view of the system. By injecting

water into a sediment bed, via outlet orifices in a buried pipe, a

zone of fluidized sediment can be developed. The zone will extend to

areas of the bed such that the upward pressure force exerted by the

injected water equals or exceeds the weight of solids and liquid above

the pipe.

In the unfluidized state, the sediment, due to its soil struc­

ture, will remain in place as long as the channel slope is less than

the angle of repose of the sediment. Fluidizing the sediment destroys

the soil structure of the sediment bed and reduces the angle of repose.

2

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-. ...

Sediment

.. ··· ..

Silted Channel

Bottom

. . .. · ... ~ \ ...

Silted Channel

Original Channel

Outlet Orifice

u~ ~z~ng

Liquid (Inflow)

.. :. : .. .. . ... ..... .. .. . .. . . ....... . . . ... · . · ....

.. ' . .. . .. ' -. .. . .. ..... . : ..

.. . .. , __ :: .. .. . .

I

. ·~Blt,t.h:l.i,"Zirlg.·P:i;pe .· ·. • ·. . . . . ""'. \ . . . '. .

., :· .. .. .. ....... · ..... ·

sz

I : • . ' .

Fluidized Zone Boundary

Fluidizing Pipe

Fig. 1 Fluidization Applied to Sediment T~ansport

3

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-. ..

The fluidized sediment behaves as a liquid and "flows" on small

slopes, (S) such as those likely to be encountered in channel bottoms.

The fluidizing liquid need only exert sufficient force to

fluidize the sediment, while actual transport of the sediment is

caused by gravity forces acting down the natural channel bottom slope.

The sediment flows down the slope to an area where shoaling is less

harmful and is then redeposited.

For clearing navigable channels, a prediction of top width,

depth, and cross-sectional shape of the fluidized channel must be

known to determine the feasibility of the planned fluidization system,

Figure 2 shows a typical fluidized channel cross section. The flui-·

dized sediment zone results from a given discharge through the sec­

tion. This zone can be described by top width at the original bed

surface; depth at the center of the zone; and zone shape described by

the fluidized boundary.

For a given sediment, it is expected that depth of pipe

burial, outlet orifice configuration and upward flow through the

section all are parameters affecting the top width, depth, and shape

of the fluidized channel.

It is the object of this study to determine how the above

parameters affect the size and shape of the fluidized channel.

4

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. . . . . ' ' .

Width

Original Bed Surface

depth

·Fluidized Zone Boundary = f(x,y)

Outlet Orifice

Fig. 2 Cross Section of Fluidized Chinnel

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. ,

..

1.1 Theory of Fluidization

Several general fluidization literature reviews are available

( 1 13) at present. ' Herein, only those areas of research associated

with the immediate problem, applying fluidization to sediment trans-

port, will be reviewed.

Two phenomena can generally be associated with a fluidized

bed; pressure in the bed and expanded bed length. By examining the

pressure in the media and the length of the bed, the effect the

fluidizing flow rate on the bed can be evaluated. Figures 3a and 3b

show the variation of both pressure and bed length with increasing

fluidizing flow rate.

Wnen water is passed through a porous media, a loss in fluid

pressure results. This loss is characteristic of the flow resistance

encountered during passage through the media. By defining the resis-

tance as a drag force, it can be seen that the resistance is propor­

tional to the velocity of flow through the media. (l3 )

In the unfluidized media, an increase in flow rate results in

a linear increase in pressure according to Darcy's Law (Figure 3a).

Eventually the force exerted by the pressure becomes sufficient to

support the weight of the media particles. The velocity of flow

through the media at this point is called minimum fluidizing velocity

If flow is considered as it passes through flow paths in the

media, each path of a given area, the discharge at minimum fluidizing

6

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. ,

-.

(a)

(b)

(JJ

H :l Ul Ul (JJ

H P-c

/ /

/ ,

B /

/ /

A

G

/ Not / • Fluidized

/ Fluidized

Qmf Flow Rate

Qmf Flow Rate

Uniformly Graded Ideal Bed

Fig. 3 Variation of Pressure and Bed Length for Fluidized Beds

7

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--

velocity can be expressed as the product of the channel areas and

velocity, Vmf· This discharge is shown in Figures 3a and 3b. In­

creasing the flow rate beyond Qmf causes expansion of the bed and

enlarges the areas of the flow paths, allowing the velocities in the

flow paths to remain at minimum fluidizing velocity. (3 ) The expan­

sion of the bed then enables equilibrium to be maintained between the

drag force and the particle weight of the media.

The behavior of the pressure with increa~ing flow rate can be

illustrated by plotting pressure versus discharge (Figure 3a). With

increasing flow rate through the media, pressure loss in the fluidi­

zing liquid increases linearly for the unfluidized bed. After fluidi­

zation occurs the pressure loss remains constant with increasing flo•~

rate.

If bed length is examined, the opposite trend occurs (Figure

3b). For the unfluidized bed, the bed length is constant with in-

creasing flow rate. Once fluidization occurs, however, bed length

increases with fluid flow rate.

The point at which bed expansion begins and pressure becomes

constant for increasing flow rate is shown as point A in Figures 3a

and 3b. This point defines the condition of incipient fluidization and

is unique for a sand of given specific gravity and particle diameter.

In a graded sand, a distinct point of incipient fluidization (point

A) does not exist. Instead there exists a range of various minimum

fluidization velocities required for the different soil fractions. (l)

8

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This is shown as line BC in Figures 3a and 3b. It can be expected

that the more uniform the gradation of the bed, the more distinct

will be the point of incipient fluidization. For the purposes of

this tehsis, incipient fluidization conditions are defined by point

A. This assumes minimum fluidizing pressure (Pmf*) and flow rate

(Qmf*) of an ideal uniformly graded bed.

Channelling and spouting are phenomena that occur in fluidized

beds at or near incipient fluidization conditions. Channelling is a

self-propagating discontinuity in porosity of the media. (l) Since

the channel develops as a path of least resistance through the media,

a majority of the flow tends to flow through the channel. Although

difficult to explain by analytical predictions, channels can readily

be seen in actual fluidized beds as preferred flow paths through the

.media. Since channelling tends to disrupt the uniformity of fluidi­

zation of the media it is an undesi~able phenomenon.

Spouting can be visualized as a special case of channelling such

that the channel extends from the flow source to the bed surface.

Wnile undesirable for the purposes of this study, spouting has been

investigated in detail as it relates to chemical engineering applica­

tions. (9 ) It is sufficient to note that spouted bed theory appears

to best describe the behavior of the pressure in the media for the

fluidizing system near incipient fluidization conditions.

9

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...

. .

1.2 Sediment Transport using Fluidization - Proposed Applications

Although literature pertaining to fluidization techniques and

processes in general is in abundance, the application of fluidization

to sediment transport appears to be only of recent interest. Litera­

ture pertaining to the specific problem of sediment transport appears

to originate with the study at Westport, New Zealand by Hagyard et

al. (5)

Sediment deposited by littoral drift causing san bar formation

has long been a problem in the harbor at Westport. In the past,

solutions to the problem have been in the form of extensions to

the harbor moles to intercept the littoral drift. (5 ) Experience has

shown this only to be a temporary solution. As permanent solution,

Hagyard proposed that a portion of the sand bar be flu:Ldized to

create a channel to intercept littoral drift and allo·..v it to "flowtt

out to sea. The proposed system included a fluidizing pipe buried

3.5 feet deep and extending 7000 feet from the breakwater to deep

water. An estimated 49 million cubic yards of sand could be removed

annually by this system while only a constant 96 H.P. would be ex­

pended to pump the fluidizing liquid through the pipe.

In addition to providing an initial design for the fluidiza-

tion system, Hagyard et al. demonstrated that fluidized sand will

flow on slopes as small as 1:400, the typical sea bed slopes at

Westport.(5 ) This is important if the system r~lies on gravity as

the sole transport mechanism to move the fluidized sediment.

10

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...

..

. -

Hagyard et al. also relied on a self-burying design for the

fluidizing pipe. Proper orientation of the fluidizing orifices would

allmv the pipe to fluidize the sediment immediately belo\v the pipe .

The weight of the pipe would then force it to sink in the fluidized

sand. Experiments in the laboratory showed the self-burying concept

to be a valid method of burying the fluidizing pipe. Ho\vever, actual

pilot studies determined that roots and objects below the surface

hindered the self-burying ability of the pipe. (4 )

Channel cross-sectional studies accomplished by Hagyard et al.

were approached in an empirical, manner. Using a perspex model to

simulate a cross section of the fluidized channel (Figure 4), he in-

jected water into a sand media via a jet oriented vertically down.

Assuming a triangular channel cross section, Hagyard et al.

described channel size by the depth of submergence of the pipe and

the angle of divergence of the channel walls. The angle of divergence

of the walls is defined as half the bottom apex angle of the channel

cross section.

Hagyard et al. further defined a quantity of flow called

"leakage" in his experiments. (S) Leakage referred to liquid that

was released to unfluidized portions of the bed. Hagyard et al

determined by dye studies that leakage occurred along horizontal and

downward paths and theorized that it tended to stabilize the sides

of the channel against fluidization. (5)

11

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..

....

\.

' ' ' ' '

' ' Unflui"d~ed

Water

I /

/ / /

/ / ./

/

,---~-.:.....-Angle of /

D. / ~verge}lce

./ /

.............. ...... Sand ---

......

...... -- ------

.... ...... ._. __

/ ....... ----~ ---·

./ ./

/ /

/ / /

/ /

/ 1 ft

- Leakage Path / ..... --- ---.._ -- --- --

./ L---------------~ /

Fig. 4 Perspex Model used by Hagyard et al.(S)

12

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Results from experimental efforts indicate that for a constant

burial depth of the fluidizing pipe, leakage decreased rapidly with

increasing flow rates of the fluidizing liquid. (5 ) Further experi-

mentation by Hagyard et al. revealed that as flow rates increased,

the angle of divergence increased. (5 ) Although it appears that flow

rate, leakage, and channel width are interdependent, no continuous

expression has been presented to describe this result.

Wnile Hagyard et al. addressed principally the cross-sectional

development of the fluidized channel, others have investigated longi­

tudinal development of the channel. Wilson and Mudie(l6) of Scripp's

Institution of Oceanography applied Hagyard's et al. fluidization

technique to create an open channel between a slough and the Pacific

Ocean. The major problem in their endeavor was maintaining flow of

the fluidized sediment through the channel. One consideration that

had not been anticipated was the formation of a delta at the channel

outlet .. · The resulting blockage in flow necessitated constant removal

of the delta to. allmv passage of the sediment. Of major importance

was the tendency for the~ channel to degenerate into a series of

"boiling holes and dams that migrated in position". By increasing

the depth of burial of the fluidizing pipe, the number of holes

decreased and the spacing of the holes increased. As a result they

defined the concept of the "flo\ving fluidized channel". In order to

develop a "flowing channel" it is sufficient that only the tops of

the holes overlap.

13

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-.

- .

Fluidization as proposed by Hagyard et al. has been suggested

to enhance the effectiveness of beach replenishment systems. One

such system is the "Crater-Sink Sand Transfer System". (l) The system

relies on a suction type dredge with its inlet located in a crater on

the ocean floor. As dredging proceeds sediment falls down the walls

into the crater to be transported to the beach. During dredging~

material continues to fall until the crater enlarges such that the

angle of the crater walls coincides with the angle of repose of the

bottom sediment. By fluidizing the area around the crater, the

effective area of the crater can be increased without substantially

increasing the depth of the crater. Figure 5 depicts how fluidiza-

tion techniques might enhance the Crater-Sink Sand Transfer System.

A method of sediment transport using fluidization techniques

has been proposed by Inman and Baillard of Scripp's Institution of

Oceanography. (B) The name of this method, "Duct Flmv Fluidization",

arises from the shape of their fluidized channel. Instead of fluid-

izating sediment above the fluidizing pipe, they propose the creation

of a fluidized channel, or duct, directly below the pipe (Figure 6).

This system is used in conjunction with a crater, or sink, to provide

a location for deposition of the fluidized sediment. In this system,

fluidization is used to suspend sediment in the duct. The transport

of sediment through the duct into the sink is accomplished by the

momentum exchange as the fluidizing liquid impinges on suspended

particles. The sediment above the pipe is eroded and replenishes

sediment transported through the duct. Due to sediment flowing into

the duct, a lowering of the channel bed surface results.

14

~-- • -.- .··· ' -- ~- ---- ,.._...,. .• _ . ._.. • •. --~- 'l:'r .. -':"'"'"'"",._..,_, .... ~--·-:'1""".-~- -- ~ ·.- '-, w,., ~--· -· ..--~. ~ . ,..... . - " ... ~- .•• ":'- -~ ---:.·· :.""::"·:;: .--; ..... .._ •••. • .. -v-- \" ~- . _:--·-. ~ ---·-

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PMN

Extended Crater Sink Crater Sink due to Angle of Repose

I

sl~

Crater Sink

Consolidated Soil

.. Fig. 5 Crater-Sink Sand Transport System(l)

15

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..

. .

The duct flow method is not fluidization as Hagyard et al.

proposed. Increased energy requirements appear necessary over that

required for Hagyard's et al. system since th~ fluidizing liquid

provides the transport mechanism for the sediment.

While it appears that some research has been accomplished

. (5 16 17) toward applying fluidization to sed~ent transport, ' ' none of

the investigators have satisfactorally addressed the problem of cross-

sectional channel shape. Hagyard et al. provided experimental insight

into cross-sectional shape as it relates·to depth of submergence and

fluidizing flow rate~ However, little has been acco~plished in deter-

mining the effect of outlet orifice direction on channel shape.

Herein, the problems of prediction of the channel cross-sectional

shape will be addressed in order to define the effect of flow rate,

pipe submergence, and outlet orifice configuration on the cross-

sectional shape of the fluidized channel.

Problems concerning the linear discontinuity of the fluidized

channel(ll) will not be addressed. In order to determine why the

discontinuities occur and how to prevent them, the basic mechanisms

of the fluidizing system must be known. It is thought that a detailed

investigation of the cross-sectional development will yield this

information.

1.3 Approach

Since fluidization requires that an upward pressure force be

exerted to support the weight of the particle bed, it seems reasonable

16

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Water

Channel B-e-~-.. ---.-.-.------.. ---~-,_~--,l •"" -: .. ·. , . . · .

· .. . .. ; : ...

Orifices . ·- ... Fluidized Sediment

........... . ·

Fluidizing Pipe . . ..... .. . ·: .· ..

.. • • • 0 ... -_, . . .. ~ " .... . .. . ~ . • • •• ....... - • .. •• •• 0 ...... ·-~ • •• . . .

Angle of Pipe

: ·: .. ; : ····.'.J .··• .. : __ :._:

.. Fig. 6 Duct-Flow Fluidization

17

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I

·-

to investigate the behavior of pressures in the media as they relate

to fluidized and unfluidized portions of the media. This is accom­

plished by both analytical and experimental methods for different

configurations of fluidizing pipe.

Analytically the equations must indicate pressure in the two

conditions; unfluidized and fluidized media. Referring to Figure 3a

a seepage flow approach applying Darcy's Law is used to define the

rising portion of the pressure versus discharge curve. The pressure

of the constant portion of the curve is calculated by a force balance;

equating the pressure force to the weight of solids and liquid in the

fluidized column.

The seepage approach has limitations in that the equations are

valid only for the fixed media. Once reorientation of the particles

begins the equations are invalid in describing pressure distributions

in the media. However, Darcy's Law provides a valid solution method

to conditions in the media prior to particle movement. It is thought

that these conditions may indicate how the media will eventually

fluidize.

The pressure distributions obtained using seepage analysis are

representative of a particular total pressure loss through the media.

By increasing this pressure to a typical fluidizing pressure, a

series of locations in the media are obtained where fluidizing pres­

sures are present. Fluidized zones obtained in this manner are then

compared to experimental results.

18

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An experimental apparatus is constructed to enable measurement

of pressures in a cross section of the fluidized channel. Pressure

distributions measured in the apparatus are compared to analytical

pressure distributions, and fluidized zones measured in. the apparatus

are compared to an analytically determined fluidized zone. Finally,

an evaluation of the validity of the seepage equation predictions of

cross-sectional channel shape is made.

19

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2. THEORETICAL ANALYSIS

The problem to be analyzed is the prediction of a fluidized

zone for particular fluid flmv rates and fluidizing pipe configura-

tions. In predicting the fluidized zone it is the pressure at a

point that determines whether or not the media fluidizes. The cruX

of the problem is then to determine the pressure distrigution in a

media resulting from the flow injected by a fluidizing pipe.

The physical problem is illustrated in Figure 7. The fluidi-

zing pipe is shown buried at a depth, d, in the silted channel. The

known parameters of the flow situation are: flow rate; soil hydraulic

and conductivity, specific gravity, and porosity; depth of burial;

and orientation and configuration of the outlet orifices on the flui-

dizing pipe.

As shown the flmv situation is bounded on three sides by the

original impervious channel walls and bottom. The fourth boundary is

the silted bed surface. In analyzing the boundary conditions then the

flow situation is bounded on three sides by a constant flow along

the boundary and on the fourth side by a constant head determined by

the depth of water above the bed surface.

The solution to the pressure distribution must be divided into

two parts; pressure in the unfluidized bed and pressure in the flui-

dized bed. This is necessary since the development of Figure 3a was

based on the concept that the point of incipient fluidization (point

A) occurred as a discontinuity in the pressure variation for an ideal

20

.. ·:---·.- ~,· .,..,.. ....... - .-,

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-..

..

lvater

\ Fluid iz~ Zone

\ \ \ \ 0 \

"- --Impervious Boundaries

/

I

I I I

I I

/

Fig. 7 Seepage Analysis Flow Situation

21

r ••••

.:

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""' ""

bed. The pressure variation prior to incipient conditions varies with

flow rate. After incipient fluidization, however, pressure depends

only on the weight of the particle bed.

2.1 Pressure in the Unfluidized State

The pressure in the unfluidized state is determined by a .

seepage analysis of the flow situation shown in Figure 7. The basic

equation for flow through a porous media is Darcy's Law:

where Q = fluid discharge

Q =o -KA dh dt

K =o hydraulic conductivity of soil

A = area of flow path

h = head

t = length of flow path.

Co~bining Darcyts Law and a continuity equation:

V.q=O

where 'V = differential operator

q = discharge vector

~ields the basic equation of motion in a porous media. This equa-

tion can be written as the steady state Laplace Equation in two

dimensions:

22

(1)

(2)

(3)

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. .

,.

Two theoretical models are offered which solve the Laplace

Equation subject to boundary conditions in the flow situation

(Figure 7).

2.1.1 Analytical Model

A literature search of two dimensional flow problems yielded

the analytical model to be used. Derived by Muskat, (ll) the analyti-

cal model is a solution to well flow in a porous media.

The flow situation solved by Muskat is shown in Fig. 8. In

the figure a well is being supplied by a stream at a specific distance

from the well. It is assumed that the flow situation is unbounded

except for the stream boundary and that all flow to the well origi-

nates at the stream.

The formulation of the mathematical model requires that the ·

well be replaced by a point source and that the stream boundary be

replaced by an equipotential surface. In Figure 8 a coordinate has

been placed on the physical situation such that the well lies on the

y-axis at (0, -d) and the stream lies on the x-axis.

In order to mathematically develop the x-axis as an equipoten-

tial Muskat locates an image sink at (O,d). Using the method of

images the potential function at any point in the media (x,y) is;

(4)

23

---- ~ 4~---~ - -.. - . ..,. - -~· .............. -. ": .. ..-·:;- ·- --, ·-: _ ..

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r

Image Sink (O,d)

Point Source, 0 (0,-d)

Fig. 8 Muskat Analysis of Fluidizing System for Unbounded Flow

24

_I

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where ~ = potential

M = strength of source or sink (q/2;)

radius to source

r 2 radius to sink.

The radii, r1

and r2

, can be expressed in terms of x, y, and d:

The equation for the mathematical model can then be written

by combining Equations 4 and 5:

where cp = potential

K= hydraulic

h = head

q = flow per

(x,y) = location

(0,-d) = location

=

rn = -Kh = ....9... Pn fx2 + (y+d )2

T 'V ~~~ + (y-d)Z"" 2n

-Kh

conductivity

unit thickness

of point

of well.

Muskat's model can be easily adapted for the flow situation

(5)

(6)

in Figure 7. The well can be replaced by the fluidizing pipe and the

stream by the bed surface. The only simplifying assumption that must

be made is in fitting the unbounded flow situation of the model to the

bounded conditions of Figure 7.

25

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.•

To fit the physical boundary conditions shown in dashed lines

(Figure 8) only the flow between bounding streamlines in the model

will be considered. The bounding streamlines chosen for this study

are those that encompass the full top width of the physical situa­

tion .. (AO and BO) as shown in Figure 8. The exact correlation between

the bounded and unbounded situations is developed in Section 4.1.

The mathematical model can detect the effect of variations of

the flow rate, depth of burial of the fluidizing pipe, and hydraulic

conductivity of the soil. There is no parameter, however, to account

for configuration of the outlet orifices on the fluidi~ing pipe. In

using the mathematical model it must be assumed that effects of orifice

configuration are only local to the area around the pipe. In this

respect the mathematical model can only approximate the physical

problem.

2.1.2 NQmerical Model

A numerical model(lO) can be used to directly solve the Laplace

Equation. The numerical model is a computer program designed to solve

the differential equation of motion by a finite element analysis.

The finite element analysis allows the media and fluidizing

pipe to be represented by a grid configuration shown in Figure 9. By

refining the grid in the area of the fluidizing pipe, the shape of

the pipe can be represented by triangular finite elements. The node

points at the pipe surface represent locations of outlet orifices on

the fluidizing pipe.

26

. .__ .... ··- --··· ..

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The model has the capability of including more than one media

material in the analysis. Using this feature, the impervious boun­

daries of the physical flow situation are simulated by a material of

extremely small permeability. In a like manner, the finite elements

of the pipe are composed of a nearly impervious material.

Initial conditions in the media can be specified as either

a piezometric head or flow at nodes in the finite element grid. For

the problem shmvn in Figure 7, the bed surface boundary condition is

supplied to the model as constant piezometric head at the surface

node points. Boundary conditions at the fluidizing pipe are deter­

mined by the outlet orifice configuration. By properly applying

either peizometric head or external flux at points A, B, and C, in

Figure 9, the outlet orifice configurations are varied.

The numerical model allows a more exact representation of the

physical flow situation. Boundaries can be exactly duplicated and,

in fact, must be included for the model's analysis. The fluidizing

pipe also is better represented in the numerical model than in the

analytical model. By choosing the proper grid refinement the size of

the pipe and its interference of the seepage flow paths can be repre­

sented. Applying proper boundary conditions the physical outlet

orifice configuration can be duplicated.

2.2 Pressure in the Fluidized State

The pressure in the media after fluidization is determined

by a balance of the forces between the weight of a column of media

27

. -.-""' ; ...

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.r

I

Hater P-al 1

Ha terial 2

7)

~ In sert A

Haterial 2

Insert "A"

Fig. 9 Node Configuration for Finite Element Analysis

28

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·.

l ' i t

and the upward force exerted by pressure in the media. It is assumed

that contribution of shear forces in the media to the resistance of

motion of the particles is negligible compared to body force (weight).

Referring to Figure 10, the sunullation of forces can be written in the

y-direction as,

where P = pressure force

W = weight.

L:F =P-W y

In the analysis the column is considered to consist of both

(7)

solid particles and the water contained in media voids. The column

of media in Figure 10 has a finite length, 1, and area, 6x~z. The

weight of that column then is the SQ~mation of the volumes of water

and solids in the column multiplied by their respective unit weights.

(8)

where W= weight of column

.t= length of column

t...x~z = area of column

ys = unit weight of solids

y :::z unit weight of water w

e = porosity of media.

Equation 8 can be rearranged to reflect the submerged weight of the

solids and the weight of a water column of dimensions 1 x (~x~z),

W = .t(~x~z)(l-e)(y ""Y ) + y .t(~x~z) s w w (9)

29

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y

Bed Surface X

Fluidizing Pipe

Fig •. 10 Force Balance to Determine Fluidizing Pressure

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. .

..

The pressure force in Equation 7 can be described as the

pressure in the media acting in an upward direction on the base of

the column. This force can be written as,

P == p (b.xb.z) (10)

where P = pressure force

p == pressure at base of col~~n

b.xb.z = area of column.

In order to fluidize, the summation of forces in Equation 7

must equal zero. Clearly, the pressure force then must equal the

weight of the column. Equating Equations 9 and 10 yields,

P (b.xb.z) -== t(b.xb.z)(l-e)(y -y ) + t(b.xb.z)y s w ·w

Rearranging Equation 11,

where p ·- pressure in media

s = specific gravity of s

yw = unit weight of water

t= length of co lunm

e = porosity.

t(l-e) (S -1) + t s

solid

Equation 12 represents both the pressure due to the weQght

(11)

(12)

of the solids in the column and the pressure due to hydrostatic forces •

The hydrostatic force is constant for a given length of column and,

therefore, can be arbitrarily eliminated from the analysis. This is

31

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...

accomplished by defining a pressure, p*, that encompasses both.

contributions to the pressure:

p~: = p + y t w

(13)

The equation for prediction of the fluidizing pressure can be

written by combining Equations 12 and 13,

P* -= t(l-e)(S -1) s

(14)

The fluidized zone in the media extends then to all areas such that

the pressure in the media equals or exceeds P*.

2.3 Results of Analysis

Pressures in the flow situation (Figure 7) were calculated for

unfluidized conditions by the theoretical models. Figures 11 through

14 show the pressure distributions obtained for each of four fluidi-

zing pipe configurations. Shown in dashed lines are the equal pressure

contours obtained by the Muskat model.

Each contour represents a nondimensionalized pressure~ To

formulate the contours, the maximum pressure on the pipe surface is

divided by 10. Each contour then represents an incremental pressure

increase, starting at zero at the bed surface, of 0.1; P being the

m aximun1 pressure.

A comparison of the pressure distributions of models provides

insight to conditions at incipient fluidization. One can note that

32

-- ---,... ....... ··-· -~~-------~-~. ·- ... ~-- .. - .. --:-··.,·.;r<...:r,.•··~-- .... · .• -.o-- ·-"':·-·· .----~··- ·-:·•--':""''' --~ .... ;''""·---;~·---:·· •. •

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. . .·

Fig. 11

\

\

I \ \

\ \

\ \

\

\ \

\

\ '\

\ \

\

'\.

I I \ \ \ \

'\.

"'-..

'\.

·" "'

\ \

'\

"' "

/ ---- -

--- ------

-- --

Theoretical Pressure Distribution - Dist. 1

. 33

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l I I I I \ I I

I \ I \ I

I \ /

.- / I I \ / \ \ \ /

\ \. /

\ \ \ \ \ ' '-\ \ \ '-... /

\. -\ \ '\.

\ \ ' \

\ \ \ \ \ \ ~

..

......... ........

.........

\ ..........

<lJ --0 --C1j \ -ll-l $.-4 \ ::l Ul

"C) \ ().)

\ r:Q

\ \ \

\ \

\. .

" .

" Fig. 12 Theoretical Pressure Distribution - Dist. 2

. 34

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... I \ \ \

Fig. 13

T

\ \

\ \ \ \

\

\ \ ~

I \ \

\

\

\

\

\ \

\

~

" "' Theoretical Pressure Distribution - Dist. 3

35

/

/ /

.

--- --

Page 44: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

I \

\

~

~ ~ ~ \ \ \ \

\

I \

\ \

\

\

\ \

\

\

\ \

\ \

\

"'

I

/

_..........,. -- - ---

---

Fig. 14 Theoretical Pressure Distribution - Dist. 5

36

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.-

..

the tendency of a column to fluidize directly depends on the pressure

gradient through the column. Thus, assuming that pressures throughout

the media are increased uniformly, the vertical sections of the high-

est pressures gradients will be the first sections of the media to

fluidize. It will be these sections that determine incipient fluidi-

zation conditions in the media.

Figures 11 through 14 show that the highest vertical pressure

gradient in the media occurs in the column directly above the fluidi­

zing pipe. Examining the pressure gradient in this column of media

will indicate how the incipient conditions vary with the models. The

nQ~erical models all indicate a smaller pressure gradient than that

indicated by the Muskat model in the area above the pipe. It can also

be noted that the pressure gradient in this area increases with pipe

configuration representing distributors 1, 2, 3, and 5 (Figure 18),

respectively.

In the formulation of the models, pressure is determined as it

varies with flow rate. It is expected then that the incipient fluidi­

zing flow rate increases as the pressure gradient critical to fluidi-

zation decreases. Conclusions can be made, therefore, about incipient

fluidizing conditions for the theoretical models:

Incipient fluidization velocity varies with outlet orifice

[( configuration

I' '

2. Incipient fluidizing velocity is lowest for the Muskat model

and increases for configurations 5, 3, 2, and 1 in that order.

37

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.-

..

An indication of the eventual width of the zone of fluidi-

zation can be obtained by examining the pressure distribution in

the media as a whole. In order to make comparisons between the models,

a "width" of the pressure distribution is defined. This "'vidth'' is

defined as the distance, at the elevation of the pipe, from the center

of the pipe to the contour representing 0.2 P.

It is expected that for a greater "width" of the pressure

distribution, a greater top width of the fluidized zone results.

Comparison of the models on this basis shows the "width" of the pres­

sure distribution of configuration number 3 to be similar to the

Muskat solution. In order of decreasing "width" the numerical pressure

distributions can be listed as configuration 5, 3, 2, 1. The respec­

tive top widths for the fluidized zones are expected to compare simi­

larly to the distribution "widths" for the theoretical models.

Fluidized zones predicted by the Muskat model are shown in

Figure 15. The zones are calculated by an iterative technique that

solves Equations 14 and 6 simultaneously. In the figure, C is a

parameter that varies with applied flow rate:

where C = plotting parameter

Q = flow rate

C = Q/2 ~ K

K ~ hydraulic conductivity •

(15)

Figure 15 shows how the predicted fluidized zone varies with

flow rate. As expected, the fluidized zone becomes larger with

38

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increasing flow rate. However, from the figure, it can be seen that

the increase in the top width of the fluidized zone is not a linear

function of C.

· Numerically, fluidized zones were calculated for four fluidi-

zing pipe configurations (Figure 18). Comparison of numerically pre-

dieted pressures at the maximum experimental flow rates (Section 3.3)

were made \vith predictions of P* (Equation 14) to determine the flui-

dized zones. The results of that analysis are shown in Figure lSb.

The top widths of the numerically predicted zones for the different

configurations of fluidizing pipe compare as expected.

From the analysis it is concluded that a fluidized channel

shape can be calculated by the theoretical models.

In addition to predicting channel shape, the models also pre-

dieted pressure in the media and flow required for incipient fluidi-

zation to occur. The analysis model must be altered to account for

outlet orifice effects.

39

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c 2

c 2.5

c 3

c =: 4

c 5

c 6

c 7

c Q/2 n K

-.

. • .. Fig. 15a Fluidized Zones Predicted by Muskat Equation

40

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.-

0 - Dist. 1

b. - Dist. 2

0 - Dist. 3

0 - Dist. 5

. -··

Fig. 15b Fluidized Zones Predicted by Numerical Hodel

. 41

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3. EXPERIMENTAL INVESTIGATION

3.1 Apparatus

To investigate the analytical predictions, a sand model is used.

Shown in Figure 16, the model is a box, 48 inches long, 28 inches

deep and 3 inches thick. It is constructed of ~ inch thick plexi­

glass with the joints glued and screwed together. To provide rigidity

to the front and rear faces of the model, one inch steel box supports

span the length of the model at intervals of approximately 9 inches.

Appendix A contains construction details of the sand model.

Discharge of water from the model is controlled by an overflow

weir and an outlet valve (Figure 16). The overflow wier is 2 inches

wide and 4 inches deep with a capacity to discharge in excess of 455

cc/sec (the maximum discharge tested). To enable complete draining

of the model, a valve is located at the base of the model. Both the

weir and the valve discharge to a disposal reservoir, with a 30

gallon capacity for storage.

In order to determine pressures in the media, thirteen pressure

taps are located on the rear face of the sand model. Locations of

the pressure taps (Figure 17) are chosen to provide a refined grid

of taps close to the distributor yet completely cover the flow regime:

A standard spacing of 4" between pressure taps is used in the region

subject to fluidization.

The pressure tap is manufactured from ~ inch hexagonal brass

stock (Figure 17). The exterior- of the tap is machined such that one

42

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. '

Disposal Reservoir

Inflow

.......... ,.,..... """" ............

..... ..... ) ·yt ~

Piezometric Columns

Overflow c:r-------------------~~1 Wier II S2.

-,,---~----

13 Pressure Taps "O"

Box Supports

Drain L Valve (r-

on Rear Face II ., II ;·:· . , •.. . . . . . . . . ,. . I 1---:.----.....l•--:-:--:------..-l

'' •, •+.'•' ' ' ' •, ,1''' • '• • • ' . • • .. ' • ·. I • . . .... ""~'· .... +· .. ·· + ....... ~·.:, ...... '·.· !\, .. :.._::·~:: ... :'·~: .~ ...... ::,.,·

.- . ·- ., . . .. ., .... ·, ..... · +' - :. .· ' .. '· II : .. : I • " •• ~-• ~ • • • ... • , •• ~ • 0 • "' ' •

• • • •• - • •• • ... I •• +' .· +"" - Ill ... : . • ·•· ,... ... , : ' ' • • • "' ' I • '• 'f": • ' • . . . . : , . . . .. , . . . "~ I . . . .. •, . . , ~: • ••• :' .... : •• •' • • •• "f. I ·• .. \. I • • • - ""'.· .. ,. ·;.·· .. : .... ~-....

:-. ' .... ... ·+ .·.·. ·. . -. ' ..

' : .,

Distributor

••• '• .... •••• 0 ,.·

l .• • . .. •.

I

. '

I I

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end screws into a ~ inch standard thread and the other end accepts

1/8 inch Polyflow Plastic tubing. The tap is screwed into a plexi-

glass block, 1~ x 1~ x 3/8" thich which is, in turn, glued to the face

of the model. The tap, when glued in position is flush with the

inside face of the model wall. The inside diameter of the tap is

1/16" to minimize problems of clogging by particles. During experi-

mentation, however, it was found the taps required cleaning occasion-

ally.

The pressure taps are connected by 1/8 inch Polyflo plastic

tubing to a 6~' manometer board manufactured by Aerolab Supply Com-

pany. This particular manometer board was chosen because it c.ould

easily be converted to provide 20 piezometric columns. Using the

above apparatus allowed simultaneous readings from the thirteen

pressure taps.

Water is injected into the media by a distributor simulating

a portion of the fluidizing pipe (Figure 16). The distributor is

constructed from 1~ inch diameter p.v.c. pipe (Appendix A). It is

3 inches long with the ends capped to fit perpendicular to the viewing

faces of the sand model. A ~ inch tapered thread is tapped into the

distributor to allow it to be screwed onto the inflow pipe. Outlet

orifices drilled into the distributor, are the same size and spacing

as those used by Mudie and Wilson;(ll) 3/32 inch in diameter

at 1 inch intervals.

44

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4" 8" 4"

3"

lf3 + 112+ lfl-t

lfl3+ lfoll+ I #6 + f.~s+ 1!4+

I

lf8 + If? + 1112+ lflOt I

if'} +

3"

~· Standard Thread

1/8"

Hole 1/16" Diameter . ,J.

1~ x 1~ x 3/8" Plexiglass

Fig. 17 Locations and Detail of Pressure Taps

45

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By varying the location and number of outlet orifices, five

different distributors are constructed (Figure 18). These distri­

butors are as follows:

1. Distributor No. 1 - 3 orifices directed downward

2. Distributor No. 2 - 6 orifices directed 45° from horizontal

3. Distributor No. 3 - 6 orifices directed horizontally

4. Distributor No. 4 - 3 orifices directed vertically upward

5. Distributor No. 5 - 9 orifices directed horizontally and

vertically downward.

The bulk of experimentation was conducted with distributors

1, 2, 3, and 5. Distributor No. 4 was used only for the measurements

of incipient fluidizing flow rate and fluidized channel shape.

The main consideration in the design of an inflow pipe is the

prevention of piping in the media at conditions below incipient

fluidization. Actually, piping along the inflow pipe was only a

problem when distributors Nos. 1 and 4 were used. To prevent the

piping in distributors 1 and 4 and to not interfere with outlet

orifices in distributors 2, 3, and 5, two different inflow piping

schemes are used. The inflow scheme used with distributors .No. 1

and No. 4 is shown in Figure 16 by the solid lines. Shm\ln in dashed

lines is the inflow piping scheme used with distributors 2, 3, and 5.

Both. inflow piping schemes provided satisfactory service during exper­

imentation with the sand model.

46

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3 Holes

3/32 11 @1"

6 Holes

3/32". @1"

Dis t. 1

9 Holes

3/32" @1"

6 Holes

3/32" @1"

3 Holes

. 3/32" @1"

5

Fig. 18 Distribtitor Configurations

47

Page 56: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

Flow is supplied to the model via a 3/4" diameter flexible

hose. A pressure regulator is installed in the laboratory supply line ( to insure a constant pressure in the supply line. A shut off valve ~

is located between the flexible base and the inflow pipe to allow

regulation of the flow to the experimental distributor.

Two sands \vere used during experimentation. Initially a fine

sand with a mean grain size of 0.14 mm arid specific gravity of 3.1 was

used. Problems with bulking during fluidization and clogging of the

pressure taps caused abandonment of this sand in preference to a

coarser media. The sand used for the remainder of experimentation has

a mean grain diameter of 0.4 mm.with a uniformity coefficient of 1.37.

A mechanical analysis of the sand is given in Appendix B.

Sand placement in the model is accomplished under saturated

conditions to insure an isotropic media in the model. Rodding of the

media is used only to eliminate large voids that have occurred during

placement. Care is taken that flow channels are not created during

the rodding process. When in place it is assumed the media is at an

uncompacted porosity. Prior to experimentation the media is leveled

to a predetermined depth. Between tests, sand is added to replace

media lost to the disposal reservoir.

3.2 Test Procedure

Itemized below are the steps taken during the fluidizing tests

in the sand model.

48

Page 57: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

1. Bury the distributor to the desired desired depth in the media.

Backfilling of the media is conducted as mentioned previously.

.. 2. Open the inflow value slowly to fill the model. Care is taken

not to fluidize to media during this operation. Shut valve off

when model is full.

3. Purge all air bubbles from the tubing and piezometric columns.

Check columns to see that gage "zero" is at the water level in

the model.

4. Open valve slowly to allow flow through the distributor. Read

and record pressures indicated by piezometric column. Also, (

volumentrically measure and record flow from the overflow weir.

5. Make observations as to channel development for the flow rate

and record.

Steps 4 and 5 are repeated as required to give a detailed ·

discription of how the pressures in the media vary with flow rate ..

Steps 1 through 5 are repeated for each distributor to note how the

pressures in the media vary with distributor configurations.

A typical test for a given distributor configuration includes

7 to 13 different flow rates. It is necessary to choose a small

incremental flow increase initially to determine incipient fluidi-

zation conditions. After fluidization fewer readings are required

since the pressure changes are small.

The maximum flow from each distributor, as limited by distri-

butor head loss and inflow capacity, is measured along with the maximum

49

Page 58: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

fluidized channel shape. At this point it is assumed that inflow

capacity available to all distributors is the same; distributor con-

figuration alone then limits the maximum flow available for fluidiza-.. tion.

3.3 Experimental Data

Tests were run on each of five distributors for a fixed depth

of burial of 12.75 inches to the center of the distributor.

Data from distributors 1, 2, 3,· and 5 are tabulated in tables

1 through 4. The data in Tables 1 through 4 represent the pressure

in the media for varying flow rates as measured at each of the 13

pressure taps. It should be noted that pressure taps 12 and 13 were

added after the test of distributor No. 1, hence, these pressures are

absent from Table 1.

Table No. 5 summarizes the incipient fluidization

and maximum fluidized channel \vidths for each distributor. Also

listed are areas of maximum cross section of the fluidized channel.

3.4 Additional Experimental Tests

After conclusion of the fluidizing tests additional testing

was conducted to examine the seepage flow patterns generated by each

of four distributors.

50

Page 59: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.. •

Table 1 Experimental Data - Distributor No. 1

Flow Rate Pressure in Media (in H2o)

(cc/sec) 1 2 3 4 5 6 7 8 9 10 11 12 13 t:1

27.48 . 1.3 1.1 0.9 2.2 2.1 1.8 3.3 3.0 5.1 3.1 1.1 Ill rt Ill

39.32 1.7 1.7 1.4 3.3 3.2 2.5 4.9 4.6 7.2 4.5 1.7 H> 0 ~

56.47 2.3 2.4 2.1 5.0 4.9 3.7 7.3 7.0 11.2 6.9 2.5 '"tf 0 !-'• ::s

72.40 2.6 2.6 2.4 6.0 5.9 4. 2 8.9 8.7 14.0 8.7 3.0 rt en

t-'

87. 62'>'c 3.0 2.7 2.2 5.3 5.1 3.7 8.0 7.8 10.5 7.2 3.0 N

Ill ::s

126.67 3.1 3.1 2.6 5.8 5.8 4.2 8.6 8.5 11.1 8.0 3.0 p...

V1 t-' t-' w

255.71 . 3. 0 3.1 3.1 5.7 5.7 4.2 8.5 8.3 10.7 8.7 3.0 z 0 rt

J-:3 *Denotes Incipi~nt Fluidization Ill

"' ro ::s

Page 60: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.I

! .. } .

Table 2 Experimental Data - Distributor No. 2

Flow Rate Pressure in Media (in H20)

(cc/sec) 1 2 3 4 5 6 7 8 9 10 11 12 13 ' ;j

26.11 1.0 1.1 1.0 2.3 2.2 1.8 3.5 3.3 6.5 3.4 1.5 2.2 1.0 '

35.83 1.4 1.3 1.3 3.0 3.0 2.5 4.8 4.6 8.9 4.5 1.7 3.0 1.4

42.86 1.5 1.6 1.5 3.5 3.4 2.9 5.6 5.3 10.4 5.3 2.0 3.4 1.5 i

' (

50.00 1.8 1.9 1.8 4.1 4.0 3.5 6.8 6.4 12.6 6.3 2.4 4.1 1.9 1

64.14 2.2 2.3 2.2 5.2 5.0 4.5 8.8 8.1 15.1 8.0 3.0 5.3 2.2

! 88. 75~'( . 2.7 2.8 2.7 6.6 6.5 5.8 11.1 10.5 15.5 10.8 3.8 6.8 2.9

V1 j N

,! 88.75 3.1 3.0 2.7 6.5 6.4 5.4 9.6 9.4 11.8 9.0 3.5 5.9 2.6 .t .I .'). ' ~ 163.80 3.0 3.2 3.0 6.5 6.4 5.2 9.6 8.7 11.3 9.0 4.1 6.8 3.0 ·i

376.00 3.5 3.5 . 3.5 6.7 6.7 6.7 9.5 9.5 11.0 10.8 4.5 . 7. 6 3.1

*Denotes Incipient Fluidization

Page 61: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

..

Table 3

Flow Rate

(cc/sec) 1 2 3 4

9.595 0.5 0.5 0.5 1.2

21.11 0.7 0.7 0.6 1.7

28.24 0.9 0.9 0.8 2.2

35.14 1.1 1.1 1.0 2.6

42.05 1.4 1,.4 1.2 3.3.

64.14 2.2 2.1 2.0 5.1 \.J1 w

74.19 2.6 2.5 2.4 6.2

81. 70-1( 3.0 2.9 2.7 6.8

94.74 3.1 3.1 2.6 6.3

380.95 3.6 3.6 3.6 6.1

*Denotes Incipient Fluidization

Experimental Data - Distributor No.

Pressure in Media (in H20)

5 6 7 8 9

1.0 0.8 2.0 1.7 2.6

1.6 1.3 2.8 2.5 4.0

2.1 1.7 3.8 3.4 5.3

2.5 2.1 4.7 4.2 6.8

3.1 2.6 6.1 5.5 8.8

4.8 4.1 9.3 8.4 12.5

5.9 4.5 10.8 10.1 13.5

6.5 4.7 11.4 10.9 13.6

6.2 4.3 9.0 9.1 10.5

6.1 6.1 9.0 9.1 10.5

3

10 11

1.6 0.7

2.4 1.0

3.1 1.3

3.9 1.5

5.0 1.9

7.7 2.8

9.1 3.3

9.6 3.5

8.2 3.2

8.5 5.0

12

1.2

1.8

2.3

2.8

3.5

5.2

6.0

6.3

5.5

9.0

13

' --~· I

0.5

0.8

1.0

1.3

1.6

2.4

2.7

2.8

2.4

4.0

Page 62: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.. · ..

Table 4 Experimental Data - Distributor No. 5

Flow Rate Pressure in Media (in H2o)

(cc/sec) 1 2 3 4 5 6 7 8 9 10 11 12 13

19.93 0.7 0.6 0.5 2.0 1.8 1.4 3.1 2.7 5.8 2.6 1.0 1.8 0.8

31.69 1:.1-. 1.0 0.8 3.1 2.8 2.2 4.9 4.5 7.8 4.0 1.5 2.8 1.2

36.54 1.3 1.2 1.0 3.4 3.1 2.5 5.6 5.1 8.7 4.5 1.8 3.1 1.3

41.54 1.5 1.4 1.2 3.9 . 3.5 2.9 6.3 5.8 10.2 5.1 2.0 3.5 1.5

51.08 1.8 1.7 1.4 5.0 4.5 3.8 8.1 7.5 12.9 6.6 2.5 4.4 1.9

62.75 2.3 2.1 1.9 6.2 5.7 4. 7 10.1 9.4 15.4 8.2 3.0 5.4 2.3 \J1 +"

75.20* 2.5 2.4 2.0 7.0 6.1 5.1 11.5 10.5 15.9 9.1 3.3 6.0 2.4

85.71 3.2 2.9 2.3 6.4 6.4 4.9 9.6 9.5 12.0 8.1 3.2 5.4 2.4

96.76 3.5 3.5 2.6 6.7 6.7 5.4 9.4 9.6 11.2 8.1 3.2 5.2 2.6

136.30 3.5 3.6 3.1 6.5 6.7 5.8 9.1 9.4 11.0 8.3 3.1 5.4 2.8

163.64 3.5 3.6 3.4 6.5 6.7 6.3 9.2 9.4 11.0 8.2 3.4 6.0 3.0

455.00 3.2 3.2 3.2 5.8 5.8 6.0 8.4 8.1 10.0 9.9 4.4 6.7 3.0

*Denotes Incipient Fluidization

Page 63: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.-

Table 5 Summary of Experimental Data

Incipient Maximum Maximum Fluidizing Haximurn Channel Channel

Distributor Flm-1 Rate Flow Rate Width Area Number (cc/sec) (cc/sec) (in) (in2

)

1 87.62 255.71 11.5 165.75

2 88.75 376.00 20.0 340.00

3 81.70 380.95 28.0 392.00

4 74.17 274.29 11.0 67.10

5 75.20 455.00 21.0 360.00

55

-~.-_,_._ ...... ,. ·-· •- --•,•-,-.,~--, .. --·-·:-• ..,--:......_-- ••• •• • • .• ·····;-r-.o:""'" .. '•~-····. ..... -- .... - ••.• - .... - ~~""!~";'_....- •• -;.·"·--:-:-... -.-~ ... ~- ··-:·---"' .... _ .......

Page 64: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

- .·-

This investigation necessitated the use of visual techniques

to trace the flow lines. A series of dye tracing tests provided the

optimum method of studying the flow lines.

The dye chosen for the tests was crystalline Postassium Per­

manganate, a strong oxidate leaving a purple trace. Because all

streamlines diverge essentially from a point at the outlet orifice,

it was physically impractical to attempt introducing dye at the dis­

tributor and tracing flow lines to the surface. Instead dye crystals

were placed at distinct points on the surface of the media and water

was pumped out of the media via the distributor.

The results of the visual investigations are shown in Figures

19a and 19b. The photographs in the figures show distinct streamlines

resulting from dye tracers. From the photographs, the effect of

distributor configuration on seepage pattern is apparent. The most

promenent effects, as would be expected, are at the distributor sur-·

face. By noting the converging point of the streamlines in distribu­

tors 1, 2, and 3, it is easy to determine the outlet orifice location

for the distributor. The streamlines for distributor 5, however, do

not appear to converge at two distinct orifice locations. Instead

the streamlines intersecting the distributor are spaced over the

region between outlet orifices.

A more subtle effect can be seen on the shape of the flow

regime for the different distributors. This effect is most apparent

when comparing the flow regimes of distributors No. 1 and No. 3. The

56

- -· --... ··-:·-::---: .. .-::.-·-::":·--~~~..,..~~- ... ~.-·.•<1' ··-· --,-- .,. ...... ~- ·-·-::·."' -- ....... ,.-.:c·-_,. •.. ·--.. ~-. :"'"'

Page 65: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

Fig. 19a Experimental Results - Visual Studies

57

Page 66: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

----~------------------------------------

Fig. 19b Experimental Results - Visual Studies

58

Page 67: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

flow from distributor 1 is directed downward and it is seen that the

bottom flow line is distorted by the bottom of the model. The same

flow line for distributor 3 is clearly at a higher elevation in the

media. This indicates the same percentage of total flow passes

through a smaller area for distributor 3 than for distributor 1.

Hence, for the same flow rate, velocity through the media would be

higher for distributor 3 than for distributor 1.

The visual tests are useful in the determination of the actual

seepage patterns of the various distributors. Additionally, they give

subjective indications of eventual fluidized zones and are presented

for that purpose. Actual determination of the fluidizing effects on

the media depend on pressure variations in the media and must be

approached by analyzing pressure distributions and not seepage pat-

terns. ()

59

Page 68: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

rr- .. -

4. DISCUSSION OF EXPERIMENTAL AND ANALYTICAL RESULTS

4.1 Comparison of Experimental and Analytical Flow Rate

In the study thus far, flow rates for the analytical and

experimental models have not been equated. The Muskat model given

by Equation 6, uses a discharge equal to the flow rate in an unbounded

flow situation of unit width. The numerical analysis and the experi-

mental model require the discharge to be equal to the flow rate in a

bounded flow situation. An adjustment must be made then to equate

the discharges if comparison is to be made between the models.

The first adjustment to be made is the reduction of unbounded

discharge to fit the bounded flow analysis. A simplifying assumption

is made at this point. It is assumed that the boundaries of the

flow situation coincide with a streamline in the unbounded flow

pattern and that only the percentage of the total flow contained

within the bounding streamlines is used in the bounded analysis.

By studying the Muskat stream functions it \vas determined

that the streamline that emerges at the intersection of the bed

surface and confining boundary gives the best physical representation

of both the numerical and experimental boundaries. This streamline

is shown as line AOB in Figure 7. ~

By manipulating the Muskat stream function,

60

·;:,• ~··• ,._ .,_ ~.- • - ~ •• <r-:".T". ,--,._ •' .~. • .__.. -:"'<,. ·~ .• ~··

Page 69: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

i""f•v •• • ·-.:- • •

where 'i' flow for streamline

q = total flow

-1 el = tan x/(y-d)

-1 ez ;:::: tan x/(y+d)

d ;:::: depth of burial,

the percentage of the total flow bounded by the streamline is

determined. Using the coordinates of the point at the boundary-bed

surface intersection (point A, Figure 7), the bounded flow adjustment

then is made:

q = 0.32 q b m

where qb ;:::: flow through bounded situation

q = flow in Muskat equation. m

4.2 Variation of Pressure with Flow Rate

The variation of pressure with fluidizing flow rate is dis-

cussed in Section 1.2. In that discussion reference is made to

Figure 3a, representing the pressure variation for an ideal bed. A

series of similar graphs has been developed and is presented to depict

the pressure variations at various locations in the media.

In the course of this study pressure variations in the media

have been investigated both experimentally and theoretically.

Figures 20a through 20m show the results of experimental and mathema-

tic endeavors to determine pressure at a specific location in the

media as it varies ~vith flow rate. The line in the figures shows an

61

--- ~ • -·. ·.·-·· .. ·- ··- -·· - .. -· . ---= --·---:::-·. ·-·· ..• - -·

Page 70: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

. '

1-:j ,.... OQ . N 0 ~ H-+ I +: I ;

I I

!:%j ~ ! I I I

I I -jl I I I I I I ' ; !

'-! X "0

I I ! I l I I i I I

(1) i I I I ' I li

j ,.... ., ,, a ., (!) ..

' ::J "'d ~-; rt li

3 ·~ ~ (1)

I ' I

' I ' I I I i I

" I I I ' I I

I I

~ I 1 1Cr~- ' I I I -...... ill

ill "'d (:: li li

0\ (!) (1) N ill

ill ,...... (:: ,.... 2 li ::J

:·l (1)

::r: <:: N ~ 0 li '-"' 1-'• ~ rt ,....

1 0 ::J

~ rt

"'d 0

l ,.... ::J

' rt .. ;

~- ' I I ~

--t+ I I ' i ,-- "11 ,- ·-- 1 r -~---~

~t- ~ -q--!~=- ' ' I

, I a: ·::F I r~ TT . -/, . ' I I i I I I I

l# ~f=li=. I I I I

=tt~'"l : -- -!-"--1 I I I

-!-±[;8 . I I ' I

-~-r-,-L ---,-- + H-· I

I ! ~!- •_f I I I -ID+ ' ll 'I r I I • I

~-.,-. ~-H- I I I -rJ=tr - , - ~ l±~+ I+++ -,--, ' - I

++-++ ~+r+ ' ~-· I -1-t+r ~-H, +++ r·- ;-;ri· T d- -+HT

J·!- I

~-±tlt -I+H-H-=R=r I I

--1 H-_ti __ t~ Rtf+ R~+ r 1 ' -i+t-l- ! I ' I 1-++ --rr

- -0 50 100 150

I ...... ..

'i '•!

:

I i

I I

I : I I I

I ' I

' I

I

i I ,rr: I I I

' -. ;-r ·- ., I tl· -r

I I I

I

' I

I I ! ; I I

' I

I I I I

i +r- I

H- ' I

' '-t-

! I ' I

200 250

Discharge (cc/sec)

I -H-' I ' I

I I

' I

I

' I

' ' - --· I ,-

I

' ' I

0 D. 0

- 0 1 --

H:~"' -~-Hl ITT

I I I 'I

I I I I I

, I I

I ·-f-f

. •.

¥ 1 L.ti+H-•J' I'

FR Ff-iTli I

-++++~tnt d:t±+ 1-rl-ri 11JP::+H:r

~~]-=f I: L.

-:I·++ +H+ -t-H-r

·.I

#$= ~ =+t-1-@ l+ ....;_-.:11, I I •lf1 1 ! I I

+ ,-1,++ -rl-1 '

! I ft +-+ ...., I l-l-l-h+i- • t +--:-· ,. i- I "1 i ·--1 I r· ---; n: r · r I

--r-t- -'~tj:+!--h-r-f- -f$H IT T+=a:tr~t-+=1+~-~-p--1-.-+--J:tll --t-t-1•-H~rf+=+R+

't If!= LEGEND =en+ r+E± -- D1st, No. 1~ -- Dist. No. 2 ;-1 I I I

Dist. No. 3m -- , I I

Dist. No.· 5 b-H 1 -- Ill ' -- Theoretical ~-n-n--'-t+" . '·-~' W-E_~~--ffi I I I I I~~~ I - - ~ -~ -c+ -, . t=FJ=J=r~a- l=

-H+J-:- I t-t I I ! I "' ,_ I ri- ,--rr;----

300 350 400 450

Page 71: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

~-----

j ' • I

. '

>->:! ,.... OQ

!'-.,)

0 o"

1:'1 X

'U ro ti ,.... a ro ;:I '"d rt ti OJ ro t-' Cll

Cll '"d c:: ti ti

•; 0'\ ro ro w Cll

Cll ...... c:: ,.... ti ;:I ro

::c: <: !'-.,)

OJ 0 ti ....., ,.... OJ rt ,.... 0 ;:I

OJ rt

'"d 0 ,.... ;:I rt

!'-.,)

.I

p[p[~~++~++~~~~p[p[p[~~++~~~9999~p[p[~~+++++++4~~~p[p[p[~:f-~f+f-·~~++~1-HI~I~I~I~~Ii ~~ ~1 H1 ~~++~~~~~++~~~~~++~~~~~++~~+H-~++~~-rrr~-~~~~-rrr++++1~~-rr1 t±:~~~~~-

I I I I I I

I I I

i I I I I

I

14-++~~-r~~++~~~~i-r++~~-r~H-++~~~-r~r+++~~~+~++++-H~-r+-rr+++-H1~~-r~~·+:+ ~~- i 1 1

1

1 I

I ' I I I I ! I I I I

I I I I I I I I i I I !

I I I I I I I I

I i

I I ' I t+H- I : I I I

I I

' i : I I I

I I

' I 1/i I r l I I I I

I I I :4- I

I

:-1 ·l/~-j· ' + · C r H+ , "'' 1 -H-h--H+H--1-H r I+ j - T"- '/,

1

1 ' . I . ,-,

1 I . , 1 I I I

l±i::b_ '+l::c<pz.pr~t±l:: R-+ H- t, --~-=t-l=i-t-=l=f-i-=1=-t+~1-~tt=Ftt~~!-lrJ::l+ ttt-J- t\41rr-t::l::l_-b ' H~rri-H[.::t · -+IITI-rti !TT 1-TIH-l]::)-i-j-2 1--n , ~·Til r-1· --rrrr- 1 , 1 1 :-rn- 1-rn- -r•ll

+H+ 11( I : LEGEND ·g +H+ H,%~~ I I ' ' : H--,-cl.:::-~_:__j__ 1

1 1 0 -- Dist. No. 1 W-1!~ iLL "-'WD· D. -- Dist. No. 2 ,

1 1-t-Tr-i:Slr:-'T 1 0 -- Dist. No. 3 ..,;,__,__rr~,~ t~9,:_~TF +

1+--f-.H-·H-r++++H1 ~~~·H-+-H-r+++-H++-l-r-l~++++++~~+-l-H 0 -- Dist. No. 5 =l=f

. ::j-r-~ 1 : -1·~~~~~~~~~-H-H-H-H-H-r-J+t~~~+t-H~~~ -· -- Theoretical SJ$rt-::jr~ -j-F +Ft_K+R=+-: --l-f-H-+r::t:t-+~+i -t-;:i_r-:T f-Hr--+t!-,t+11-+l=t.:t.tt~t=i~-t.tt~t=i.::f-t-H-t++-=+-r-+HH-+-+-n-+1 -t--H~+H-/-t ~tl+R+l=i=RtJ-4::~Ftt#/i /n=h ! +!- --I+R H+ I 1

1 1 r II . ' 1 1 -1-i+R=l=R-n-

' .. 0 so 100 150 300 350 400 450

Discharge (cc/sec)

Page 72: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

N 6 n

I • .. ,

'"d '"1 ro (/) (/)

c 1-i ro

I T1 I ' I It

' I I I I I

I I I I I I I

I I u_j..J_ f.-~ I ! I I I ' I -l- I I I I I ! I

I I I H-l--f-1 f-t-j'---HI-+-+-+-+-H--H--H-++1+ J+ I+ I JC-a±J=+-U :+Dt.p H1= fB-~ , H--+-+-+-H-1 -H-+-+-+-HI +~---~-~ -+-H--HI-+-+-+-+--H---HH-1 ~-~-~+t-FH+t-n-- r-t+-H- R=R-- -I i , T .

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l I I I : I I I I I I I I I I r I I I I I I I -: I ! ! __ __;_r-1-f+f-~:+

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1 11--f-!--!-j1-+-+-+-+-H-+-b-H-+++f--+-1 ++H-H-+ 0 -- D 1St • N 0 • 1 i¢

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2

0 50 100 150 200 250 300 350 400 450

Discharge (cc/sec)

Page 73: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.

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t =~ 1 - -r-H-+ ;--rrr Z til m til til a>

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65

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Page 74: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

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66

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Page 75: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

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Page 76: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

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Page 77: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

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'"'d >:: r; r;

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6 ji_ ~~- + =-~ t:tl:t:l=l--=1= - + I -1- I I L 1-l 'F-R=' ± 1-:f-=l~=t:r-, + I . 1_ -t/A'-- - -+- + -·-+irj"""-+ -·-f.--1 ,-()1 1-j-IJ'--h- H-+++1++-i-t-t-1-t-t++·++.-+1-1- +t-t-t1+H-+t-H1-I-t-1 H-H-11-1-t-HI - + : ' , j

\.0 (I) (I) ....... >:: 1-'• r; ;:I ro

::I: <: N Ql 0 r; ~

1-'· Ql rt 1-'• 0 ;:I

Ql rt

'"'d 0 1-'• ;:I rt

~~~- -!- J/J:t- -- ,RJ:::R+I _j.+-+-1-+t-+-+-li t-+_).::::~-+--:Hf--+~1:--::-~~ +H--+ +-t-t+ H-· ++-1++-H-tl- J + il+=ft:-3- -l- ~=R= -~-- +1--R=FF ~~- 1 ! I I I 1

1 I

1 _1 -~J-+ i , 1 + 1+ , r~:-8t 4 rw~~~~ ' ,' , ' ' LEGEND Cl:l+

~~ '1 --!' 1

1

1 f-1- : -~ H-' -l 1 1 0 -- Dist No 1 ~~

~:::\~~- ; ~I+_+'· , lr-trl ~-t-:=F - + T -~ ~~-!- I _-~,~- f--+-1 I -- • • 2 f+h+ j~-1 H-t-1 I I I I I I I I ~~ ,-,I I ' ' - + 6 Dist • No • I I

2 j~~ f.--} _j._ H++ u... · D -- Dist. No. 3 1; = -- - £ r : 1+ r+H+ +f+f - 1 + ++-FFFI=·- - --- 0 -- Dist. No. 5 Hu....u-t-t_-H

: = - .It I ' rTH-t--FH-F 1 I ' ' 1 , - -- Theoretical H-++-

lkf=t,:::~tf ~it,-ti~$t •= ttf~ ff+ ,=~~~iilf-f i~;~r- :~tl~ttl~~!t-ft$~t~· 00 0 50 ·---Too 1SO 200 250 300 350 400 450

Discharge (cc/sec)

Page 78: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

N 0 1-'•

'"d ti CD (I) (I)

~ ti CD

~ ti 1-'• Ill rt I-'• 0 ;:I

Ill rt

'"d 0 1-'• ;:I rt

\0

,....._ 1-'• ;:I

::t: N .0 '-"

~',

, , -~, r·1 1! '1 1 · i I I Ji I I I

. ' I 1 i ml rn-;--;T,j:: I I I I 1l--P-=-IT11 tTfi --~~~ I

H-+++++-+-H-t-t 1.-+-H-l-H-+++-+-+-H-·t-~ ~ ' I I =r:l-~+~-r' I I l L-n~- ::_11--!-,-1-16 -,, r l r r 1, , r r 1 , r 1 1 , , ,. , : , , 1

1 _j_ I t- W- H- ~~~ tiz!--! i : I r,-~-+ -1 I I I I I t+h---!-t-c-H-t--W-: h-;- ~ !--] + RT- H-- i-tt .r- -1\-l +1-!-1!-H-+·++++~• I H+ I -H--l-++++-1-+1++,1++-1+--l-;-1-- h-~!-1--h , .. · ··i I '-,-- I ' Q,-- ~J H- '-rH-H-++--H-l-l-+++-+-H-+-H-t-J_j-_j-jj~~---~~--· ,-i-r-rl-+t-H-l±J-j·r·H+ Tr_,_,_ . + 4-- r-Ai· -H--l I i+- H- r-~-~: j-. I r1TI:Tr:-r-~]T ' I I I I d 1-

- IT' f/_ I - I I ' I ' I +- --' -r- :. :=;: I i II lf- -H-H-1-f-1-H-H-+++++++-!--H++-l-ri-+-l-+-+-++++++-H-H-H-HI-l-H-l-1 -1--l-' +-+-1 ++1+-1-1+ 1+1-1--l-t- -9-~e--j--:-j-+-

;1++-H-1-+++-t-++-H-1 I I ,=FR= r: -1 t _j_+t 14 ' 'p

6

I I·

~

H-+-1--H-H-H t I

I ,..I .,

! I I I

;..;. 1/"t i '' 'c'l

-li-1-H--1-1 +-1+ I ~++-+-+-+++-H+--l-+4, ,.., I .L.

I I

;:;;-· +,

: I I

'

:' ++H-=R+t= I I . I

I I

!-+-+-H---l'-1 --+1-+-++++-+,-t-1-i

I: I

i+t+ ~+-'IH-, +-+++-+: -tn-i-1H-_

~ I I i I

+H++Hi: ! I -t-HH--)_I

If I I

1+1++-H-+~1~;··~-H-1-H-+-!--~4-1-H-+++-1

I , +H+ I I

0

1' I

I 1.+1

I i 1 I

--j-1-+--: -i---1--+' -H-i,_

=t+~ -1--i-'-+->--'' -1-t--l

I :I I

I I I i I l i I

.(])_ ~ I I I i I '-1--H-+-!--H-i r+ i ; I + -t+ I --R-;+1 +++-+-+ I ; I ~+-1--!-+-H-J-+-r--t I I ~ ~ 1 ,

-t- I il=!trn -!1= --~ .~ : . -:r-H l- H I .. j~/ ::= -j . ~=~=~~=- . I -l-_i H· -H=fi-·11 I I II

50 100 150 200 250 300 350 400 450

Discharge (cc/sec)

Page 79: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

• ' 1 '

12 ! I I +:f± t-C::H- I t I !

I I

--I I I

-r -H--++ t 1::-l--r I , ' --l i-J-1 I; IT I + -+ I ' I =r+++ ~.t --rl +r-r-t- -t+--,·-j··, + r!- ' ,, H-

"%j 1-'•

()Q

N 0

t.....

~ ~ '0 {1)

li

I I '

I I I I

I

I

-- ' I

I I

r

' ', -h- ---l- I I -- -:-1 m-1+-~-=R-H-- ~--l+mj_ I I ~-Hf+±L+l n I - 1 + ~tt: T ·t--t- . -m~~-- I I -r:-1 1 , r Ti , r _LL,-;--~r-t-r -1 , 1-- 1:..ttt I , I I I I ' 1 --j---ri!T-rl!r I liT !. I ; I ;-rr;

IE, I - I I i I ' : I I I '_I ; =c-tJ~- Jl+ =t--ltt .} -- )l_vf. I ---l- : I l I + r-R==I=I=t't-~l=R -: -H+ Rtf

tt.l=tttttttttt~t:.t+lt-iift~ _J I if~+ I t #~ ~~ (j)~- ' I I+ :=t=tl1 ft-tj!:: --811= tt# --~~f =Et=~rl: )r ~H 1-;;r<Pt-- TIT I iT '- . -j r:· - ;-, rr-1+ 1+1-t- I n--r--··j··l n-· -I h l T lTI

_f I· ~0 -~-H --ttH I I -- + -- H- -+++I- Ii-l q--H--i-+ L' !-. f-±±± I i ±t 8

1-'• a ro p '"0 rt li Ill CD I-' {Jl

{Jl 6 '"0 !=: li li.

""" CD CD I-' {Jl

{Jl ...-.. ~ 1-'• li p CD

:I: <: N Ill 0 li ........ 1-'• Ill rt 1-'· 0 p

.Ill rt

'"0 0 1-'• p rt

L L I i ' 1

I-' 0 100 150 200 0

250 300 350 400 450

Discharge (cc/sec)

Page 80: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

r h

I .j

,. )

·'

-...! N

N 0 ?;"

'"d ti (!) fJl fJl ~ ti (!)

5 -H I

I I

I

I I

I I I

I I .+

I I

I

H+

'' I I

r

'' I I

Ill ' ' l

n I I

1+-11-H-H-H-H-t-++1 ++++-++-H-H-1- Hll 4 -l

I I 'I

I I I

'I

I I I

'I ' I

I I

I -1-

! I

r-H-' I I I

t-t-+-++-i'-+-H-, +-+-+1-Hf-+·'-+, +1-H-1!-t-+-+, -H-+-1!-H1 1

' ++ ...,;,-t-+-t-+-H-H-t-+-1 r-r-tf- -j-+'-H-+->--H-H I 1 -J-H f-tffiT T '

. .l ... H- -~ I ' I ' I ., I I I _, LLJ ... L.'.J...J. ±: . ~FR :~~b I ' ! ' I I - LEG END 3± -,

I '1

' II~ + 1,__

1 , ' ' I

1 ~- 0 -- Dist. No. 1 . , 1 t 1 fffiP/, 1 , -, =F D. -- Dist. No. 2 S$J$

1-+11~/++h -t-J , +± ' , 1 1 '1 ,__._. _ _._

1 .....,+ 0 -- Dist. No. 3 'i-1 1.-\-:i~~-~~~--+-l-t-t-++++-t--HI--r , 1 +J-H

1-+.--+-1·1

·++,_+,1-··~t-·r~~-+-++++++-l H'=t-f+~1=!t-=FJ#: 0 -- Dist. No. 5 =Hj $; ~~;~-~~=-, -Rl=- :_; + -~ W-+1+-+-H-H; -!-'-1-+-HI -r'++h- t- ifh1~=Fiw.~=l;;_w::t.~;~ir:~:

0 50 100 150 200 250 300 350 400 450

riischarge (cc/sec)

Page 81: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

i :

.·)

N 0 t-'

t-' N

\

'"d li (!) (Jl (Jl

t: li ro

I ; I

·. 1+-t-t-. '~ I '

'i+H-+-j I i

-- t I I

I l

I I

; I I

I I

ITT I

I I

I I I

I I I ·-T-,-

. , T '

T .TTl" l_j I I I I I I I 1

1 1 : 1 :-+H-H--/--r=:t--

1 --1 l ! I

I I 1 I -1

I I, -,--,

--1-+--H;-!-H--H'-J I I

I I -L H-1 +-+-H-'~"'"r-H--­'t- ; / I+.

10 : I +HI

I l I I I I I

8

0

I I

I I I I I

I I I ! t

I , I I I:

I '

I I ' I

t r r I I 1

I I I !

I I

I I

I I

I ' I

I I

I

I I I

1 ; l r I t 1

I I

I_ I/,

r

I I

I I T

I I I I

H-:

'I ! '

·,ffi= ·I I I I

I I I

I ~I I ! I I

i! 1 I I I . I I

r; I

-rl II I I I

I'

I I I

' I II I ' i/i+ I _j - _j_l__ +-U. ; I I r , 1 r I • 1 tT ~n-... : ,1-rr

50 100 150 200 250 300 350 400 450

Discharge (cc/sec)

Page 82: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.J

.J

'I ., '

f'-' 0 3

"' l"i ro Cll Cll I= l"i ro

• ' f '

5; I I -r l I I j_( II ·1 II

3

I I

I I I I ! I

I I I '

I I

f r I I

'I

I I

II+ I :

-./++--i--1-l-1-+++, +++++++-1-t-+++-1-1--1-1-H-1--1-~+H+ + H-l---1

1--1-+'++++++++~h -r r--1

_,

+ +

I I

I I

1 r·-!- --1 1-- !--!-. t ·n j r J·- .. ::I=!T! -'r:±r . ,... . .. =t+R--

'I

-++-H1--l---1-+-H---I

1-

I'

II+

I It~

'+

-+++-J--1-J..+++-l---J.-l~ 1 I 1 I I I

I+I-+-I-++++_+,---I+-J+-tttt·~D.Lj4E-+.' j-~ I G I I I i I +-r I I++! +4--H--J--,1--1-1--1--i-++1-j-Q-f i 1 I (\;:; 1

I ., : I I I 1

I ! t- -j· }- f<A1 ~-I--+H-·-1-+f+. ++--H-J-J 2 ~~tttt'::t::t~=r=-~tf~>+ti tt:tfffi!-ti·:tt·:::;~~-l~j?t: tt±::ttijj=tttt I I I

1 :

1 ,

1 1 I I 'I [. I_ Ll-l---+--

1 W

ltl'ltl· tl' tlltf,ll'--tfl-~--~. tfltrll,-1-'"1:/+..:lyl' 11-~-~[rrrr11

llll~-~~-~~~~ 111111111

111 1 LEGEND · ~f--1 ~~ .1~' ' ' ; ' ' ' ' ' ~ :: gi:;: :~: ~ f

lf_ .. -__ ~r.r~~~ +-!+ , , I 1 , 0 -- Dist. No. 3 -. ~]{ I 1-t-+-1--1-iH-+·1--1-I=R+ 1 , '· 0 -- Dist. No. 5 CE,11 J~)t 1-f 1

-- Theoretical E8+ t -~=1-H-+-1--1-1 !-J-J-J-JI---1-H ; ' I =l=j=!=tr,q .. -1 I ' I =~~~-i '~l: I I I -f- 'rf

0 IOO 150 z-oo 250 3'00 350 400 . --'~-·-· --- ..

450

Discharge (cc/sec)

Page 83: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

! I ! I ; I r

k.·

• "

J

analytical pressure variation calculated by the Muskat equation

(Equation 6) in the unfluidized state and by Equation 14 in the

fluidized state. Experimental results are plotted as symbols in the

figures •

Agreement between the experimental pressures and the Muskat

equation are good in Figures 20a through 20i. Thus, the Muskat

equation can be used with confidence to predict pressures in the

media at points 1 through 9 (Figure 17) in the experimental model.

At points 10 and 11 (Figure 17) experimental pressures show a small

deviation from predicted pressures. This deviation can be seen in

Figures 20j and 20k. The remaining two points, 12 and 13 (Figure 17),

show even greater deviation of experimental pressures from the pre-

dieted values.

The experimental pressures follow the same general trend,

regardless of the location in the media. While in the unfluidized )

state pressures generally tise along the theoretical line predicted

by Equation 6. A peak in the pressures occurs immediately prior to

the onset of piping in the media. After piping occurs pressures I

exhibit a distinct reduction in magnitude.

With still increasing fluidizing flow rates, the pressure

behaves in one of two modes, depending on whether the location of

the point is in the fluidized or fixed portion of the media. In the

61 . nfluidized portion of the media pressures continue to increase with

flow rate. The rate of pressure increase however, is much less than

75

Page 84: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

the rate before piping. This behavior of pressure is evident in

Figures 20k, 1, m, and would indicate that the preponderance of flow

after piping escapes through the fluidized zone in the media.

At locations in the fluidized zone, the pressures after piping

should reduce to the theoretical minimum fluidizing pressure calculated

by Equation 14. As shown in Figures 20d through 20j, the experimental

pressures fall below the theoretical line. The deviation between

calculated and experimental pressures becomes greater as 1) location

gets closer to the fluidizing pipe, and 2) fluidizing velocity

increases.

Maximum disagreement between experimental and theoretical

fluidization pressures occurs at point 9 (Figure 17) in the media

and at the maximum fluidizing flows for each distributor. As noted

in Figure 20i, point 9 was not fluidized during two of the tests,

distributors No. 2 and No. 3. The maximum deviation at point 9 then

is approximately (-)20%, occurring with distributor No. 5.

Error can occur by inaccurate computation of the specific f)'(

gravity o£ porosity of the sand or from inaccurate measurement of the

experimental pressures. Porosity, specific gravity, and depth all

directly affect computation of the theoretical fluidizing pressure.

Clearly, inaccuracies in any of these variables would result in a

noticeable error in comparing theoretical and experimental pressures.

An error.from theoretical calculations would be consistent at a given

depth and would increase linearly with depth. The errors detected in

in the figures, however, do not display a regular pattern.

76

Page 85: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

I.

Another possible source of error lies in the experimental appa-

ratus itself~ At high fluidizing velocities the fluidized zone

becomes visibly turbulent. Because of small burrs on the inside of

the pressure tap or because of clogging by sand grains then it might

be expected that turbulent areas can develop at the pressure taps.

In this manner the pressure tap may detect not only the pressure due

to the weight of the ~oil but also that due to small velocity head~.

Because of insufficient time, the source of the error remains unde-

termined.

4.3 Conditions at Incipient Fluidization

Incipient fluidization conditions imply both a flow rate and

a resulting pressure in the media \vhen it first begins to fluidize.

Presented are incipient conditions evaluated both theoretically and

experimentally during the study.

As shown in Figures 20a-m, the experimental pressure at

incipient fluidization is much higher than that predicted by Equa-

tion 14. At locations near the distributor (Figures 20g-j) a dis-

tinct peak in the pressure occurs at incipient fluidization. The

peak is discussed in spouted bed U..terature (9) as a result of local

porosity changes in the media.

By examining changes in the media during experimentation, it

can be concluded that porosity changes do occur. Immediately prior

to fluidization a hole in the media develops at the outlet orifice.

Since the bed has not yet started to expand according to experimental

77

Page 86: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

...

observations there must be some way to account for the hole. Intui-

tively, the media particles must be packed more closely than normal

at the walls of the hole. This change in the packing of the parti-

cles causes more resistance to the flow than expected and allows the

incipient fluidization pressure to rise to its peak value prior to

piping.

While the peak pressure is quite different than the theoretical

fluidizing pressure, the incipient fluidizing flow rate agrees well

with predicted values. To provide a location for comparison of

theoretical and experimental values, point 9 (Figure 17) was chosen.

Being the closest experimental location to the distributor, it was

the first location to fluidize during experimentation.

The minimum fluidizing flow rate as calculated by the Muskat

mathematical model is 60.5 cc/sec. The experimental minimQm fluidizipg

flow rates range from 74.11 cc/sec to 88.75 cc/sec. As discussed

earlier (Section 2.3), it is expected that the Muskat solution would -----yield a minimum fluidizing flow rate smaller than the numerical

models. At that time it was concluded that orifice locations account-

ed for small variations in the minimum fluidizing flow rate. The ------·---------prediction of minimum fluidizing flm11 rate by the Muskat equation was

as expected; slightly smaller than the experimental flow rates.

4.4 Distribution of Pressure in the Media

The theoretical model should be capable of simulating the

pressure distribution in the media if it is to satisfactorily predict

78

Page 87: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

...

the.eventual fluidized zone. In Figures 2la through 2ld, experimental

pressure in the unfluidized media are shown with numerical model

results.

Since the numerical model contours are based on an arbitrary

pressure at the orifice, a slight adjustment of experimental pressures

is required for the co~parison. Point 9 (Figure 17) was chosen as

the "match point" and the experimental pressure at that point pro-

vided the amount of adjustment required. It should be noted that

the experimental pressures were chosen from data in Tables 1 through

4 such that minimum adjustment was required to fit the numerical

contours.

The experimental pressures, as adjusted, show good agreement

with the numerically calculated results. Exceptions to this occur

in two areas; i~mediately above the distributor and far from the

distributor near the boundary walls. The best fit bet\lleen experi-

mental and numerical results occurred with distributor No. 5. Dis-

tributors Nos. 1, 2, and 3 showed slightly less agreement between

experimental and numerical results.

The Muskat model was not used in the comparison of analytical

and experimental pressure distributions. Since the Muskat model

does not consider either the effects of orifice configurations or the

flow boundaries, it is doubtful that any comparison of experimental

and mathematical pressures would give valid results. In this respect

the Muskat model is best used as a ''standard solution" \llith which to

compare the different numerical models (Section 2.4).

~9

-· • ··- ··•:-.. - ··-.-- .. - .... -·-.- :- ~--- --.·rr-;-;-.';'"' ::--;;.-:-;o-_..--:-•-:-.·· .- ~- ... ,-.--.-.

Page 88: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

1.

1.1+

1.0+ 1.9+

+ +

*Denotes Match Pressure

Fig. 2la Comparison of Experimental and Numerical Pressure Distributor 1

80

-·-. ' .~

Page 89: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.. i

1 1

1.1

2.6

4.0+

1.1 + 2.6 +

*Denotes Match Pressure

Fig. 2lb Co~parison of Experimental and Numerical Pressure Distributor 2

81"

Page 90: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

-. ..

1.1

1. +

3.9 +

1.3+ 2.8 +

*Denotes Match Pressure

Fig. 2lc Comparison of E~perimental and Numerical Pressures Distributor 3

Page 91: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.....

-..

~----.....-t-----r----'-

1.0 3.1

2.8+

*Denotes Match Pressure

Fig. 2ld Comparison of Experimental and Numerical Pressures Distributor 5

83

Page 92: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

4.5 Comparison of Fluid~d Channels

The eventual goal of this study is to be able to predict the

fluidized channel shape given the necessary variables. Throughout

the study it is assumed the following are known:

1. depth of burial of fluidizing pipe

2. outlet orifice configuration

3. hydraulic conductivity of sand

5. specific gravity of the sand.

Knowing the above parameters, fluidized channel shapes have been

calculated using the numerical model for each of the five distributor

configurations. Shown as dashed lines in Figure 22, the fluidized

channel shapes have been calculated using the maximum experimental

rate for each distributor •

... At first glance, there appears to be little or no agreement

bet~11een. the experimentally measured and the. numerically calculated

fluidized zones. However, examining the top widths of the fluidized . ' . ' I .

channels, the numerical model predicted accurately the experiment

top widths of zones resulting from distributors 4 and 5. The numer-

ical model also predicted, ~ith some error, the top width of zones

from distributors 1 and 2 •. There is no agreement, however, in the

top width prediction resulting from distributor No. 3.

It was obser\red experimentally that at high fluidizing flow

-· ... .; rates, a,jet of flow normal to the distributor surface emanated from

the outlet orifice. This jet enlarged the fluidized zone width by

84

Page 93: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

-. •

. -

,/ --G------ - -o--;/--

-£)--- -o-

--/

/ ----0 __...[]---- -

Ex~rimental Zones

®- Dist. 1

/A- Dist. 2

m- Dist. 3

X- Dist. 4

@- Dist. 5

Numerical Zones

0- Dist. 1

b.- Dist. 2

0- Dist. 3

X - Dist. 4

0- Dist • 5

I

..........

Fig. 22 Comparison of Experimental and Numerical Fluidized Zones

85

Page 94: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

eroding the boundary walls and was particularly prominent in tests

--------------~~----··--- --- . . . with distributors No. 2 and No. 3. The numerical model has no

------~~ mechanism to account for the existence of a jet emanating from the

- .... orifice and cal~ated fluidized zones resulting from distributors

2 and 3 show the zone shape as if no jet erosion occurs. Some ~

adjustment of the calculated fluidized zones then must be made if the

numerical model is to predict the channel shape with any confidence.

---~~-

..... '

86'

Page 95: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

.. ..

. .

5. SUMMARY AND CONCLUSION

This study investigates one of the problems involved in

applying fluidization to sediment transport; that of predicting a

fluidized zone shape for a given configuration of fluidizing pipe •

The pressure distributions resulting from different pipe configura-

tions are investigated for the unfluidized state. Fluidized zones

are then developed theoretically from these pressure distributions

and compared to measured experimental fluidized zones.

Theoretically, a seepage analysis is used to predict pressures

in the media and ultimately predict a zone of fluidization. A purely

mathematical model derived by Muskat(ll) provides a "standard solu-

tion" with which to compare numerical and experimental results.

The Muskat model assumes an unbounded flow situation and considers

no effects due to the fluidizing pipe configuration.

A second analytical method is tailored for use on a digital

computer. Solving the Laplace Equation by a method of finite

elements, (lO) it provides a numerical solution to the pressure

distribution in a porous media. By variations of the finite element

grid the effects of the fluidizing pipe configuration .can be modeled.

The numerical method assumes the flow is bounded and can be altered to

fit the physical conditions •

Experimental pressures and fluidized zones are measured in a

sand model. Distributors representing five different fluidizing pipe

configurations are tested. The widest fluidized zone results from a

8.7

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distributor having two sets of three orifices horizontally opposed.

The smallest fluidizing zone results from a distributor having three

orifices directed upward. - ....

The seepage analysis yields theoretical predictions of

pressures up to incipient fluidizing conditions. The Muskat model

provides a good approximation of the variation of pressure with flow

rate in the area of the fluidizing pipe. Except at incipient fluidi-

zation, the pressures measured experimentally agree with the Muskat

prediction. At incipient conditions, however, the experimental

pressures reach a peak substantially higher than predicted.

The minimum fluidizing flow rate is analyzed subjectively and

quantatively. As a result of the analytical work, the minimum fluidi-

zing flow rate can be shown to vary for different fluidizing pipe

configurations. Experimentally, minimum fluidizing flow rates varied

from 74.17 cc/sec to 88.75 cc/sec depending on the distributor. The

Muskat equation predicts a minimum fluidizing flow rate of 60.5 cc/sec.

Prediction of the fluidized zones by the Muskat and numerical

models was generally poor. With the exception of distributors 4 and

5, the experimental fluidized zone is altered by erosion. The erosion

caused by the development of jet flow at high fluidizing flow rates

can not be predicted by the numerical or Muskat model.

.. Of the configurations tested it is concluded that the dis-

tributor having two sets of orifices horizontally opposed should be

pursued as the most practical fluidizing pipe configuration. This

88

,.... ··--... .,.. ..... ~. ·.- ~

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•.

. . ' . "

conclusion, based on observations in the sand model, is justified by

two reasons. First, the distributor does not fluidize the sand

beneath the pipe. When in operation, the fluidizing pipe using this

configuration will not sink, therefore, no elaborate anchoring system

should be required in field tests. Secondly, the above distributor

yields the widest fluidized zone for the given minimum discharge.

It is unfortunate that the theoretical analysis was unable to

predict the fluidized zone for distributor No. 3. The equations

presented provide a basis for analyzing the fluidization problem for

incipient conditions. Additional analysis is required, however, to

evaluate widening effects due to erosion before the theoretical

analysis can successfully predict the eventual fluidized zone shape •

89

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. •

APPENDICES

90

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Page 99: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

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,., 48" -----V

Page 100: FLUIDIZATION APPLIED TO SEDIMENT TRANSPORT · 2012-08-01 · 2 LIST OF FIGURES Fluidization Applied to Sediment Transport Cross Section of Fluidized Channel 3 5 3 Variation of Pressure

"":1 !-'•

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<: Ill rt !-'• 0 ;:l

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for 8 x 32 x~'' bolt 3" O.C.

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Note: (1) Box material is l" p lexiglass, base ma.terial is 3/4'' plywood. (2) All joints butted, glued, and bolted.

... . 2 •

Drill and Tap Hole 3/4" NTP

Side

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. -If..._ ..... ... , . l • •

. ..

~ \ t-'• Drill and tap 1,11

2 NPT Cap ends with 1/811 plexiglass ()Q . :X:. I w

1-rj J-' I I I= ------·--..1...--t-'· 0..

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~ as required \ t:J ,, ) t-'•

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' rt 11 - --------t-'· cr c

~ ~ rt 0 11

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.. . .;

APPENDIX B: ANALYSIS OF SAND USED IN MODEL

A mechanical analysis of the medium sand used in the experi-

mental apparatus was performed by others. To determine properties

of the sand the following standard tests were performed:

1. Dry density test

2. Specific Gravity test

3. Porosity test

4. Sieve analysis

Tables B-1 and B-2 and Figure B-1 show the results of the

mechanical analysis.

94

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/".

l

' • .i

- .

Table B-1 · Properties of Medium Sand

Dry Density

(1) Undisturbed -

(2) Compacted -

Specific Gravity

(1) SG -

Porosity

(1) Undisturbed

95.9 lb/ft3

98.3 lb/ft3

2.55

(a) porosity - .464

(b) void ratio - .867

(2) Compacted

(a) porosity - .430

(b) void ratio - .753

95

--':"- -- -_- ... -:· -:--:o -- ----

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(' • ~1

"

' ..

Sieve

Number

20

30

40

50

60

80

100

200

Table B-2 Sieve Analysis

Weight (gm) Percent Grain

Gross Tare Net Retained Size (m..rn)

467.9 467.7 0.2 0.0 .841

533.8 508.4 25.4 5.1 .590

853.5 497.2 356.3 71.2 .420

619.6 510.0 109.6 21.9 .297

481.0 474.9 6.1 1.2 .250

438.4 435.7 2.7 0.5 .178

245.9 245.9 o.o 0.0 .149

466.6 466.4 0.2 0.0 .074

DlO - .370

D50 - .480

D90 - .53

Uniformity Coefficient

cu ; D60/Dl0 = 1.37

96

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Sieve Number

200 . 140 100 80 60 50 40 30 20 10

Grain Size (mm)

...

Fig. B-1 Grain Size Distribution

- . 97

I I I I ~

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r

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I .• I· ,

I "

I ., 1:

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BIBLIOGRAPHY

1. Amiratharajah, A., "Expansion of Graded Sand Filters during Backwashing," M.S. Thesis, Ior.va State University, 1970 (unpublished).

2. Amiratharajah, A. and Cleasby, J. L., "Predicting Expansion of Filters during Backwashing," Journal of American \Vater \\forks Association, January 1972, pp. 52-59.

3. Cleasby, J. L., "Water Filtration through a Granular Media," Engineering Research Institute, Iowa State University, May 1969, pp. 33-40.

4. Hagyard, T., "Sand Fluidization Experiments at Westport," September 2, 1970 (unpublished).

5. Hagyard, T., Gilmore, I. A. and Mottram, W. D., "A Proposal to Remove Sand Bars by Fluidization," New Zealand Journal of Science, Vol. 12, December 1969, pp. 851-864.

6. Harr, M. E., "Groundwater and Seepage," McGraw-Hill Book Co., New York, 1962.

7. Inman, D. L. and Harris, R. W., "Crater-Sink transfer System," Proceedings, Twelfth Coastal Engineering Conference, September 1970, pp. 919-933.

8. Inman, D. L. and Bailard, J. A., "Analytical Model of Duct-Flow Fluidization," Symposium on Modeling Techniques, September 1975, Vol. 2, pp. 1402-1421.

9. Mathur, K. B. and Epstein, N., "Spouted Beds," Academic Press, New York, 1974, pp. 1-46.

10. Murray, W. A., "Analysis of Groundwater Flow," Lehigh University, 1973 (unpublished).

11. Muskat, M., "The Flow of Homogeneous Fluids through Porous Media," McGraw-Hill Books Co., New York, 1937, pp. 175-181.

. 12. "Fluidizing Sand to Open the Harbor Bar," New Scientist, March 19, 1970, pp. 556.

13. Othmer, D., "Fluidization," Reinhold Publishing Corporation, New York, 1956, pp. 1-20.

14. Volpicelli, G. et al., "Nonhomogenieties on Solid-Liquid Fluid­ization," Fluidized Bed Technology, American Institute of Chemical Engineering, 1966, pp. 42-50.

98.

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,

f

'

·r

. !I'

15. Watters, G. Z., "Hydronamic Effects of Seepage on Bed Particles," Journal of the Hydraulics Division, ASCE, Vol. HY3, March 1971, pp. 421-439.

16. Wilson, C. R. and Mudie, J. D., Comments on "Removal of Sand Bars by Fluidization," Scripps Institution of Oceanography, Marine Physical Laboratory (unpublished).

17. Wilson, C. R. and Mudie, J. D., "Some Experiments on Fluidiza­tion as a Means of Sand Transport," Scripps Institution of Oceanography, Marine Physical Laboratory (unpublished).

99

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r

VITA

,.. John T. Kelley was born in Philadelphia, Pennsylvania, on

August 10, 1950. He was raised in Willingboro, New Jersey, where

·he graduated from John F. Kennedy High School in 1968.

The author enrolled at Drexel University \V"b.ere he participated

in the U. S. Army R.O.T.C. program. He graduated in 1973 with a

Bachelor of Science degree in Civil Engineering and was commissioned

as an officer in the U. S. Army. In 1976 he entered a Master of

Science program in the Water Resources Division of the Civil Engi-

neering Department at Lehigh University. In his graduate program he

was supported by a U. S. Army Fellowship.

I 100