Chapter 2 LITERATURE SURVEY - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/8549/11/11_chapter 2.pdf · extensive literature survey made by the present investigation, ... phase

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experimental data on parametric study was not published. From the

extensive literature survey made by the present investigation, it was

observed that, the published literature available on the experimental

data pertaining to two phase flow through jet pumps was limited.

Either they have used dimensional analysis or incorporated various

loss coefficients to predict the efficiency of the jet pump. Earlier

researchers have not made attempts to establish a theoretical model for

mixing of the coaxial jets and the effect of parameters such as area

ratio (R), nozzle distance from throat entrance (s/dt), mass flow ratio

(M), head Ratio (N) and pressure drop on the performance of the jet

pump.

Chapter 2

LITERATURE SURVEY

2.1 INTRODUCTION

Though extensive research work has been reported in the field of

Two-phase flow, very few research papers have been published which

deal with the two-phase flow behaviour in a jet pump and the resulting

performance of the jet pump, particularly when the pump is subjected

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to interference due to short straight pipe and bends on the discharge

end. However, these are typical situations very much encountered in

practice. In order to answer such problems researchers have conducted

experiments and drawn special curves to visualise the flow phenomena

for single-phase flow. Generalized picture however is missing

altogether. With a view to find the existing gaps in the literature

pertaining to two-phase flow behaviour through jet pump a systematic

study of literature has been carried out and presented below:

2.2 AREAS OF STUDY

In order to study the problem thoroughly as envisaged in the

previous chapter the research publications available in the literature is

classified into the following areas:

i) Single-phase flow,

ii) Two-phase flow (slurry transportation),

iii) Mixing of primary and secondary jets in the jet pump,

iv) Interference of flow field due to shorter transport pipe.

It is therefore natural to examine the way in which different

aspects of the problem have been taken care of by different researchers

in the past, so as to have a comprehensive picture in various aspects of

the problem under investigation. It is obvious that, these different

aspects of study cannot be looked in isolation. They should be

examined together. Unfortunately, most of the researchers have

studied the problem in isolation.

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2.3 REVIEW OF PAST RESEARCH WORKS

2.3.1 Single-Phase FlowSufficient information on single-phase flow for fully developed

steady state conditions is available in the literature.

Two important aspects of study are:

Velocity distribution at a section,

Pressure along the flow line.

For the sake of completeness of the report, equations for friction

factor and the pressure drop is shown in Table D.1 (Appendix-D). But,

in the developing region or when there is flow interference, the

correlations predicting the flow behaviour are not available. However,

the works of Miller [67, 68] and Idelchik [41, 42] form a wealth of

reliable experimental information. With the help of tables, graphs, and

empirical correlations they presented the flow picture in a special

manner.

2.3.2 Two-Phase FlowA large number of research papers have been published since

1886 (Thompson [124]), which deal with the flow of solid-fluid mixture

in pipelines of circular cross-section. Though quite substantive

contributions are available, only the most important ones are reported

here. Malhotra [58, 59], Seshadri [114, 115] and Weber [137, 138] in

their works have highlighted the historical background of hydraulic

pipeline systems and their use for transportation of mineral ores in

various parts of the world. They stressed on the basic parameters to be

considered during the pre-design stage of pipeline transportation. Some

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early experimental works are very important in view of the care taken

during the experiments. Wang and Tullis [134] presented several forms

of friction factor equations for single phase flow. Their boundary layer

approach is used in the present theoretical analysis. Shih [117]

conducted experiments for hydraulic transportation of solids. He used

specially made wooden balls of specific gravity slightly higher than

unity, mixed with water and transported through a Lucite pipe whose

slope was varied from horizontal to 17.7 degrees. It was clearly shown

that, the effect of the slope of the pipe on the head loss coefficient

became more pronounced for higher solids concentration in the flow of

mixtures. One can study the effect of slope of the pipe on pressure

gradient particularly when the difference in specific gravity between the

two-phases is small. The range of variables in his experimental work is

presented in Table H.1 and the results are presented in Table H.14 in

Appendix-H.

Another very carefully designed experimental programme on two-

phase flow dealing with both hydraulic and pneumatic transportation is

of Rose & Duckworth [104]. The effect of change in relative density

between the phases could be studied well from his experimental data.

Rose and Duckworth’s experimental results were deciphered to validate

the present mathematical model. Their experimental results are

presented below:

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Fig. 2.1 Relationship between the pressure gradient and the nominalwater velocity for the established flow of lead shot in water in ahorizontal pipe (Rose and Duckworth [104]).

Fig. 2.2 Relationship between the pressure gradient and the nominalwater velocity for the established flow of Mustard seed in airin a horizontal pipe (Rose and Duckworth [104]).

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Fig. 2.3 Relationship between the friction factor for a suspension, λm,and the Reynolds number (Rose and Duckworth [104]).

For a general two-phase flow through ducts, a large number of

research papers starting from very early years till now are available in

the literature. In recent times Tsuji et al. [127, 128] used numerical

technique to determine the motion of a particle using Langrangian

method, assuming that the fluid phase is not affected locally by the

presence of particles except for the additional loss of pressure. For the

calculation of fluid phase, the method developed by Patankar and

Spalding [79] was combined with PSI cell model of Crowe et al. [15] to

arrive at complete flow picture of solid-gas flow through horizontal

channel. Some of the theoretical findings were compared with

experimental data obtained by using measurements by Laser Doppler

Velocimeter (LDV). Another very interesting experimental work of

Morikawa et al. [72] dealt with particle velocity and concentration

measurement using optical fibre probe.

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The duct cross-section also plays a very important role. The

experimental work of Prasad et al. [81] clearly showed that, for the flow

of solid-liquid mixture, the rectangular duct of aspect ratio 1.5 yielded

the best performance. In some earlier works Prem Chand [85]

developed particle dynamics equations in a differential form to explain

the response of particles in two-phase flow. While deriving the

equations, various resistances like friction and impact among the

particles and the particles with the wall were considered. The diffusion

equation was used to assess the distribution of Particle-Number-

Density with a view to obtain the number of particles coming in contact

with the wall. Thus at any section the spread of particles could be

obtained.

Jotaki and Tomita [45] investigated the effect of solids to air ratio

on solids velocity and concentration. A typical plot giving concentration

distribution of soyabean in a horizontal pneumatic conveying duct

viewed from the side of a 130.8 mm pipe is shown in Fig. 2.4 below.

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Fig. 2.4 Concentration distribution viewed from the horizontal in a 130.8mm pipe for Soybean transportation(Jotaki & Tomita[45])

They studied the flow patterns of solids with the help of slow

motion picture. They obtained very reliable data for lean phase flow. In

another earlier work done in the Department of Mechanical

Engineering at IIT Kharagpur by Chand and Saha [88], the feeding

behaviour of solids into a pneumatic conveying system using a slot

nozzle was explained by using the theory of re-attachment

phenomenon. Minimum distance required for the first phase of mixing

of solids with incoming air could be found from this work. Later the

concept was extended while fabricating a modified blow tank system.

Further, a theoretical model was developed to explain the two-phase

flow behaviour of the entire system. The theoretical equations were

verified by conveying materials like coal dust, rock phosphate, fly ash,

PVC powder etc. McLean [63] has suggested a procedure for blow tank

design to give cheaper operations with high efficiency. The jet pump

also works on a similar principle of a blow tank. In both the cases, the

incoming primary fluid stream entrains the surrounding solid-fluid

stream in the throat region and both move together through the

divergent duct (diffuser), which leads to the transport line.

2.4 THE JET PUMPRanga Raju [99, 100] presented a detailed review of jet pumps

after classifying them into three categories:

i). Liquid-liquid jet pumps

ii). Liquid-solid (slurry) jet pumps

iii). New type of pumps

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2.4.1 Liquid-Liquid Jet PumpsDefinition of Efficiency: Even though the general definition of

efficiency i.e. the ratio of output energy to input energy remains the

same as has been interpreted by various researchers, the final

expression of efficiency has been found to be different. It basically

depends on how they have conceived the input and output power.

The efficiency of a Liquid-Liquid jet pump has been defined by

most of the researchers as the product of the mass flow ratio (M) and

the head rise ratio (N).

Therefore,

Efficiency, η = MN

Where, M = Ratio of mass flow rate of secondary fluid to that, of the

primary fluid;

N = Ratio of the head gained by secondary fluid (Hd - Hs) to the

head lost by the primary fluid (Hp-Hd);

Hd =pressure at the diffuser exit;

Hp = pressure of the primary fluid at the entrance of the

primary nozzle;

Hs = Pressure of secondary fluid at the tip of the primary

nozzle.

Many researchers have studied the performance and design

aspects of jet pumps for single-phase flow, i.e. liquid-liquid pumping.

The works are sub-divided into two groups, viz.:

i) Central jet type conventional jet pumps

ii) Annular jet type pumps

2.4.1.1 Central Jet type Liquid-Liquid Jet Pump

Several researchers like Cairns & Na [10], Kudirka & Gluntz [53],

Rao & Goenka [101], Aggarwal [1], Gosline and O'Brien [33] have

studied and proposed equations in dimensionless parameters for

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frictional losses, impact losses and pressure drop in the throat. Folsom

[30] modified the equations proposed by Gosline and O'Brien [33] by

including the densities of primary and secondary liquids and the

suction pressure, so that the jet pump operation could be analysed

with liquids of different densities. In his analysis, he included

mechanical and thermal energy terms in addition to continuity and

momentum equations.

Cunningham [16 to 20] did extensive work on liquid-liquid jet

pumps. He reported that, the absolute pressure level had no effect on

the jet pump performance and confirmed the same through

experiment. Ueda [129] showed that, optimum area ratio was

dependent on the flow ratio. He experimentally found that, for a flow

ratio range of 0.2 to 1.0, the optimum efficiency was obtained with a

corresponding area ratio of 1.2 to 0.33. Mueller [74] conducted

experiments and proposed a theoretical one-dimensional model,

considering various loss coefficients for respective components. Reddy

& Subir Kar [102] showed that, the ideal efficiency for a jet pump is

50% at a flow ratio of 1.0. The actual pumping efficiency was found by

considering all the loss coefficients in the ideal efficiency equation. The

losses due to individual components were expressed in the form of

Darcey-Weisbach equation.

Sanger [107 to 110] conducted exhaustive experimental work on

low area ratio liquid–liquid jet pumps. The experiments were conducted

at NASA laboratories, USA. The experimental set-up consisted of a

closed loop test facility with provision for recording all important

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parameters of a jet pump. A schematic diagram of Sanger's carefully

designed sophisticated test loop is given in Fig. 2.5. It is worth noting

its salient features which are mentioned below:

i) The working fluid i.e. water was de-aerated to 5ppm by mass

before using in the system.

ii) Particles larger than 40 microns were filtered.

iii) System water temperature and pressure were controlled between

prescribed limits ( 210 C to 270C)

iv) Air content in the system was monitored.

v) A blow down system was provided to allow dye injection for

mixing studies and to calibrate the test sections for friction loss

coefficients.

vi) The flow rates were controlled by sophisticated valves.

vii) The test section was fabricated with acrylic plastic for visual

observation.

Fig. 2.5 Schematic of water jet pump test facility of Sanger [107]

The experimental parameters are as follows:

Table 2.1 Sanger’s Experimental Parameters

Parameter Range

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Primary nozzle tip diameter (dn) 8.8 mm, 15.2 mm

Corresponding area ratios (dn/dt)2 0.066, 0.197

Ratio of distance of primary nozzle tip fromthroat entrance to throat diameter (s/dt)

0.0, 0.96, 1.05, 1.36,1.54, 1.81, 2.2, 2.58,2.66 and 3.03

Ratio of throat length to its diameter (l/dt) 7.25, 5.66 and 3.54

Diffuser included angle 8.10, 60 and 2.50

Diffuser outlet to inlet area ratio 7.73, 6.25, 7.32 and2.97

Fig. 2.6 Jet pump primary nozzles (all dimensions are in inches (cm))

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Fig. 2.7 Details of main components of jet pump (Sanger [107])

Sanger’s important findings from the investigation are as follows:

i) The throat length required to complete mixing was found to be

related to area ration as well as to nozzle spacing. Longer mixing

lengths were necessary for higher area ratios.

ii) The zero nozzle spacing was found to be most efficient for both

area ratio pumps because of the relatively long throat (l/dt =

7.25). Performance at maximum efficiency levels was maintained

for both area ratio pumps over the range of nozzle spacing of 0

to 1 throat diameter, but performance decreased at larger

spacing. However, due to increased susceptibility to cavitation

at the zero nozzle spacing position, this nozzle position should

not be inflexibly regarded as the “optimum” position for this

configuration.

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iii) Low efficiencies exhibited at low flow ratios are due to inefficient

mixing, whereas low efficiencies at high flow ratios are due

largely to frictional losses.

One of the sample plots of Sanger is given below:

Fig. 2.8 Variation of Pressure coefficient (Cp) with axial location from throat entrance(x/dt) (after Sanger[107])

Rao & Goenka [101] studied experimentally, the effect of

geometrical parameters on the performance of jet pump. However,

specific conclusions could not be drawn. Cunningham [20] derived

theoretical pressure characteristic equations using energy analysis. He

extended his earlier works and derived theoretical characteristic

equations using the energy analysis for the case of nozzle distance from

throat entrance of greater than zero. A constant was introduced to

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account for the jet energy loss, which had to satisfy its value as unity

for s/dt > 0; and also had to be zero when nozzle coincides with throat

entrance i.e. s/dt = 0.

Radhakrishnan & Kumaraswamy [98] compared and tried to

match the performance of jet pumps with centrifugal pumps.

2.4.1.2 Annular Jet Type Liquid-Liquid Jet Pump

Shimizu et al. [118] experimentally investigated the relation

between configuration and performance of the annular type jet pumps.

The annular type jet pumps were compared with central-jet-type jet

pumps. They used twenty-five different kinds of annular type jet pumps

in their experiment and observed a maximum efficiency of 36%, which

is almost equal to that of the conventional central-jet-type pump. They

also studied the effect of swirl component on the efficiency of the jet

pump. They reported that, weak swirl does not affect the efficiency in

general. On the other hand, a strong swirl component caused a

decrease in pump efficiency. Also, they concluded that, a pump with

high or low flow ratio with high head ratio compared to central jet type

jet pumps could be designed by selecting appropriate nozzle area ratio.

2.4.2 Solids Handling Jet Pumps (Slurry Jet Pumps)As discussed previously, a good amount of information is

available on the performance characteristics of liquid-liquid jet pumps.

But not much data is available on the performance of the solids

handling jet pumps. The works on solids-handling jet pumps may be

further sub-divided into two groups:

i) Central jet type conventional jet pumps, and

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ii) Annular jet pumps.

2.4.2.1 Central Jet Type Slurry Jet PumpsZandi & Govatos [144] presented a design analysis of solids

handling jet pump for preliminary estimates for the geometry of the jet

pump. Fish [29] derived an equation for the efficiency of jet pumps by

making several assumptions, some of which appear to be very wild.

Wakefield & Ruckley [132] developed a speedy method of calculating

basic parameters of the jet pump for low Reynolds numbers.

Wakefield [133] designed and implemented the World's first fixed

sand bypassing scheme using jet pumps. It is working on Nerang river

mouth at Surfers' Paradise, Queensland, Australia. The details of the

project are presented here under:

He showed that, a combination of jet pump and centrifugal pump

is a better alternative in terms of energy consumption when compared

to either of them. Further, he showed that the combination of

centrifugal pump and a jet pump gives a complete blockage resistant

flow, provided that the power input to the jet pump system is at least

one-third of the total. He suggested that, subsequent sand bypassing

schemes would use hybrid system. Being a commercial project results

conclusions regarding parametric effect on jet pump are not published.

A typical submerged jet pump is given in Fig. 2.9 and the jet pump

used in Nerang river sand bypassing project is shown in Fig. 2.10.

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Fig. 2.9 A typical submerged jet pump

Fig. 2.10 Jet pump used in Nerang sand bypassing project

Mikhail et al. [66] performed experiments and reported that, the

efficiency of the jet pump increased with the increase of solids

concentration. They found optimum distance of the tip of nozzle from

the throat entrance for the jet pump configuration used. As the area

ratio increased, the dimensionless distance (x/dt) required for

maximum efficiency also increased.

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2.4.2.2 Annular Jet Type Slurry Jet Pumps

Raju, D.R [99, 100] and Weber et al. [137, 138] investigated

experimentally on air-lift and jet-lift methods and compared the

performance of both the systems, with a view to explore the possible

application to deep-sea mining. An annular type jet pump was used in

the jet lift system. Theoretical equations were developed based on

momentum and energy balance. They concluded that, specific energy

and efficiency were better for jet lift system than the air-lift system.

Duckworth [24, 25, and 104] proposed a novel pumping system for

ocean mining. According to him, a higher lifting efficiency could be

obtained by replacing air with air and buoyant particles, which provide

the necessary lift for the material. The buoyant particles could be re-

circulated continuously in a closed loop. He developed equations for

the power requirement in terms of concentration, density of buoyant

particles, mined material and the injection depth ratio. The efficiency of

the system was reported to be 60%, which appears to be much higher

than any air lift pump or jet pump.

Engerlin et al. [27] studied experimentally the performance and

erosion of an annular slurry jet pump. They reported that the efficiency

increases with the increase of discharge ratio (Qs/Qp). According to

them, sand concentration does not have a strong effect on the

efficiency. They found that the annular configuration gives a two orders

of magnitude reduction in erosion rate over the conventional design.

They recommended that the annular design is well suited to

applications where large volumes of motive fluid are available.

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Ng, K.L. [78] proposed a slurry eductor for ship unloading of

pulverized coal. It was an integrated system with a re-circulation of

motive fluid after filtering the pulverized coal with a vibrating screen.

2.4.3 Other Types of Jet Pumps

In addition to the conventional and annular jet pumps, some

researchers performed studies on novel designs, like centrifugal and

bend-type jet pumps. The details are given below:

2.4.3.1 Centrifugal Jet-Pump

Xiao [142] developed a Centrifugal Jet Pump for the hydraulic

and pneumatic transport of coarse solids. This pump has combined

basic features of a jet pump, a centrifugal pump, a hydro-cyclone and a

hydraulic solids feeder, while eliminating their various disadvantages.

The pump can work without dilution of the delivered slurry and

completely eliminating the moving parts. For the first simplest model of

centrifugal jet pump he obtained a maximum efficiency of over 30%,

and felt that the efficiency could be raised further by improved

construction. He suggested that the pump was suitable especially for

pumping coarse solids for short distances or periodic transport.

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Fig. 2.11 Centrifugal Jet pump

2.4.3.2 Bend Type Jet Pump

Yano et al. [143] conceived a

new type of water jet pump

called the bend-type jet pump as

shown in Fig. 2.12. They used

small area ratios (dn/dt)2 of

0.141, 0.165 and 0.191 . The

efficiency curves were similar to

those of the ordinary type jet

pumps. They concluded that it

could be used for transporting

liquids containing large particles.

2.5 SOME INITIAL WORKS ON PIPELINETRANSPORTATION OF SOLIDS

The present work on Jet pumping of Solids is related to pipeline

transportation and it would be appropriate to report some important

early works on pipeline transportation. Malhotra [58, 59] presented a

Fig. 2.12 Bend-type jet pump

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brief historical background of hydraulic transportation of mineral ores

and listed the various commercial slurry pipeline systems working at

different places all over the world. Further, he presented the potential

for transportation of ores in India. He also discussed the basic

parameters like - particle size, pipe diameter, flow velocity,

concentration of the slurry, viscosity - to explain the flow mechanism of

slurry transportation.

Seshadri [114, 115] too emphasized the need for considering the

basic parameters and rheological characteristics of the slurry at the

pre-design stage itself.

Weber [137, 138] presented a comprehensive overview of the

basic technology and principles involved in the design of hydraulic and

pneumatic systems for conveying solid-fluid mixtures. He emphasized

the need for a digital online system for data acquisition and data

analysis for relatively short duration of experiments. A good amount of

theoretical and experimental work was reported from time to time from

Osaka University, Japan. Tsuji et al [127, 128] proposed a numerical

simulation to determine the motion of particles and fluid in a horizontal

channel. The simulation was based on Lagrangian method for the solid

phase where trajectories of many particles were calculated by

integrating the equations of motion of a single particle. For the fluid

phase, Patankar & Spalding [79] method was used in combination with

PSI-Cell model. They measured the fluid velocity and solid velocity with

LDV, optical fibre probe and pitot tube. The theoretical results were

found to be in good agreement with experimental values at low fluid

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velocities. Many researchers investigated the blow tank type feeding

system for pneumatic conveying.

Prem Chand & Narasimha Rao [89] proposed a theoretical model

to predict the characteristics of modified blow tank system. They

conducted experiments to verify the model by conveying materials like -

coal dust, rock phosphate, fly ash and PVC powder. Madhusudana Rao

& Tharumarajan [57] investigated experimentally the fluidised gravity

conveying system and reported that materials with low bulk density

could be conveyed at relatively low pressures and at small inclinations

of 1 to 4 degrees by gravity under fluidisation. Wiedenroth [141]

conducted experiments on a model dredge pump to study the wear

characteristics of impeller and pipeline elements like bends, pipes etc.

The dependence of flow velocity on wear rate was fully established for

elbows and was found to agree well with other researchers.

2.6 MIXING OF TWO CO-AXIAL JETS

Considerable amount of work was done on the development of

free jets and mixing of co-axial jets, based on boundary layer theory.

Gibson [32] reviewed the works of various researchers. The various flow

regions identified in a co-axial jet mixing are:

Transition region consisting of potential core and self

preserving zones,

Rapid entraining zone, and

The re-circulating flow region.

Choi et al. [11] experimentally studied the mixing of subsonic co-

axial jets in ducts of constant area and variable area, with emphasis on

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the effects of an imposed adverse pressure gradient in the potential

core and transition regions. It was observed that significant radial

static pressure variations occur in both initial mixing and transition

regions as a result of turbulent normal stress gradients. Croft and

Lilley [13] analysed the jet pump flow using finite difference technique.

A turbulent model in combination with Navier-Stokes equation with

kinetic energy and energy dissipating rate as parameters was developed

and the resulting partial differential equations were solved for pressure

and velocity.

2.7 OBJECTIVES OF PRESENT WORK

The literature survey reveals that a complete hydraulic solids

handling jet lift system has so many types – each type forming a nice

mathematical challenge of its own. Many researchers have used their

ingenuity and developed their own correlations based on the

experimental data obtained by them, but they lacked fundamental and

systematic approach.

The purpose of the present work is to carry out a systematic

study on the mixing of co-axial jets in the jet pump and the resulting

flow through pipes based on the following aspects:

(i) Fundamental equations giving importance to solid-fluid flow

behaviour in general,

(ii) Mixing characteristics of solid-fluid mixture (slurry) with the

incoming pressurised fluid through primary nozzle,

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For this purpose a test-rig was carefully designed, fabricated, erected

and experiments were conducted to find the effect of different

parameters on the performance of the jet pump which is listed below:

i) Area ratio (R) – the ratio of the area of the nozzle to the area

of the throat, (dn/dt)2

ii) (s/dt) Ratio – the ratio of the distance of tip of nozzle from

throat entrance (s) to the diameter of the throat(dt),

iii) Flow ratio, (N) – the ratio of the secondary volume flow rate to

the primary flow rate, and

iv) Concentration of solids.

Further, to formulate a model based on the fundamentals and to

establish the relationship between the parameters studied by

mathematical analysis in the form of a suitable correlation. In addition

to this, it is proposed to develop a computer program based on the

above mathematical model to simulate the flow conditions.