DESIGN, CONSTRUCTION AND TESTING OF By ...

Mansoura University Faculty of Engineering Mechanical Power Eng. Dept.

DESIGN, CONSTRUCTION AND TESTING OF

By Hossam SaadElDin Saleh AbdelMeguid

Supervisors Asiss.Dr. Abdel -Rahim Dohina Faculty of Engineering Mansoura University

Prof. Dr. Mohamed Gamal Wasel Faculty of Engineering Mansoura University 2000

Acknowledgement Thanks to ALLAH the merciful, which guided us until this work, was accomplished. The authors’ wish to express their sincere gratitude for Prof. Dr. Mohamed Gamal Wasel, Dr. Abdel-Rahim Dohina for their supervision and valuable advice during the work. Thanks are also due to Eng. Hamdi M. H. Elmanzalawy for his helpful in preparing the laboratory and work shops. We would like to express our deep thanks for staff members in mechanical engineering department. May all who helped us in preparing the manuscript also receive our deep gratitude. Finally, the authors wish to thank their parents and families for their help and forbearance. Finally we beer alone the responsibility for all errors in this work.

I

CONTENTS CHAPTER 1

INTRODUCTION 1.1 1.2 1.3 1.4 1.5

Definitions Dimensional Analysis Parameters Affecting Performance of Hydraulic Machine Classification of Hydraulic Pumps and Compressors Pump and System Matching

1 4 12 14 24

CHAPTER 2

MEASUREMENTS 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

Measurements Mechanical Measurements Method of Measurements Torque Measurement on Rotating Shafts Speed Measurement on Rotating Shafts Shaft Power Measurement (Dynamometers) Pressure Measurement Volume Flow Rate Measurement Components and System Accuracy

28 28 28 30 32 34 35 38 41

CHAPTER 3 REGENERATIVE TURBINE PUMPS 3.1 Why Regenerative Turbine Pump? 3.2 How Regenerative Pumps Works? 3.3 Cavitation in Regenerative Turbine Pumps 3.4 Effect of Increasing Flow Rate on The Performance 3.5 Pump Specifications

45 48 50 53 55

CHAPTER 4

Theoretical Analysis of Regenerative Turbine Pump 4.1 Introduction 4.2 Governing Equations 4.3 The Numerical Procedure

57 58 60

CHAPTER 5 DESIGN AND CONSTRUCTION OF TESTED PUMP 5.1 Engineering Design Problem 5.2 General Procedure in Machine Design II

64 65

5.3 5.4 5.5 5.6 5.5 5.8

The Purpose of The Pump Structure of Tested Pump Forces Acting on The Parts of The Pump Material selection Forces Acting on The Parts of The Pump Manufacture of Tested Pump

66 67 67 70 73 75

CHAPTER 6 EXPRIMENTAL WORK Test pump 6.1 Description of Hydraulic Circuit 6.2 Description of The Test 6.3 Empirical Formula

79 81 85 86

Chapter 7 RESULTS AND DISCUSSION 7.1 7.2 7.3 7.4 7.5

Introduction Results of Theoretical model Results of Experimental work Correction of Theoretical Formula Specific Speed of Regenerative turbine Pump Ns

89 89 98 110 110

CONCLUSIONS AND RECOMMENDATIONS Conclusions Recommendations

111 112

References APPENDIX Appendix “I” Appendix “II” Appendix “III”

113 A-1 A-6 A-12

III

LIST OF FIGURES Fig No. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 5.1 5.2 6.1 6.2 6.3

Description Hydraulic turbine control volume Compression and expansion in compressible machine H-Q curves Axial and centrifugal pumps Centrifugal pump and its components Axial flow pump Gear pump Positive displacement pump Pump and system matching Pump and system curves Torque measurements devices Strain gage Torque measurement by optical method Eddy current drag cup tachometer Shaft power measurement (dynamometer) U tube manometer Manometers Elastic transducer Orifice meters Regenerative turbine pump Theory of operation of regenerative turbine pump Vortex in collecting passage Comparison between centrifugal and regenerative turbine pump Simple line diagram of regenerative turbine pump Fixed control volume Element in collecting passage General cell in collecting passage Pressure distribution in collecting passage Pattern of the regenerative turbine pump Test stand of the pump Pump parts and construction Torquemeter

IV

Page 6 9 13 14 16 17 21 23 25 26 29 30 31 33 34 36 36 38 39 46 48 48 54 57 58 59 61 68 76 80 80 83

6.4 6.5 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19 7.20 7.21 7.22 7.23 7.24 7.25 7.26 7.27 7.28

Variable speed electric motor Control panel Theoretical pressure distribution in collecting passage Theoretical effect of speed on delivery pressure Theoretical effect of speed on WHP Theoretical effect of mean diameter on delivery pressure Theoretical effect of mean diameter on WHP Theoretical effect of channel diameter on delivery pressure Theoretical effect of channel diameter on WHP Theoretical effect of number of blades on delivery pressure Theoretical effect of number of blades o WHP Performance curves of impeller k10 at speed 1200 rpm Performance curves of impeller k16 at speed 1200 rpm Performance curves of impeller k20 at speed 1200 rpm Effect of speed on delivery pressure of impeller k10 Effect of speed on delivery pressure of impeller k16 Effect of speed on delivery pressure of impeller k20 Effect of speed on BHP of impeller k10 Effect of speed on BHP of impeller k16 Effect of speed on BHP of impeller k20 Effect of speed on mechanical loss of impeller k16 Effect of speed on overall efficiency of impeller k10 Effect of speed on overall efficiency of impeller k16 Effect of speed on overall efficiency of impeller k20 Effect of number of blades on delivery pressure Effect of number of blades on BHP Effect of number of blades on overall efficiency Effect of clearance on delivery pressure Effect of clearance on BHP Effect of clearance on overall efficiency

V

83 83 90 91 92 93 94 95 96 97 97 99 99 99 100 100 100 101 101 101 102 103 103 103 104 105 106 107 108 109

NOMENCLATURE Q H, h N, n P gH D, d f M, L, T P

Re v A ds dv X, Y, Z n r B Qo C, Co V l k WHP BHP T F b R

ρ µ

Φ ψ θ ω

Flow rate Head difference Speed [rpm] Power Energy difference Diameter A function of Fundamental dimension of mass, length and time Power coefficient Reynolds number Velocity Cross sectional area Elemental area of closed surface Elemental volume of control volume Coordinates Unit vector normal to the surface Radius of pocket location Volume flow rate per unit length Flow velocity Volume of impeller pockets Length of collecting passage Number of pockets Water horsepower Break horsepower Torque Force Width of blade Reaction force Density Fluid viscosity Flow coefficient Head coefficient Angle Angular velocity

VI

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INTRODUCTION

CHAPTER 1

INTRODUCTION 1.1.DEFINITIONS A turbo machine can be described as any device that extracts energy from or imparts energy to a continuously moving stream of fluid, the energy transfer being carried out by the dynamic action of one or more rotating blade rows. The dynamic action of the rotating blade rows sets up forces between the blade row and fluid, while the components of these forces in the direction of blade motion give rise to the energy transfer between the blades and fluid. By specifying that the fluid is moving continuously, a distinction is drawn between the turbomachine and the positive displacement machine. In the latter, the fluid enters a closed chamber, which is isolated from the inlet and outlet sections of the machine for a discrete period of time, although work may be done on or by the fluid during that time. The fluid itself can be a gas or a liquid, and the only limitations that we shall apply are that gases or (steam are) considered perfect and that liquids are Newtonian. The general definition of the turbomachine as used above covers a wide range of machines such as ship propellers, windmills, waterwheels, hydraulic turbines and gas turbines. We will limit (1)

CHAPTER 1

INTRODUCTION

ourselves to a consideration of only those types of turbomachines in which the rotating member is enclosed in a casing or shrouded in such a way that the streamlines can not diverge to flow around the edges of the impeller, as would happen in the case of an unshrouded windmill or aero generator. Table 1.1 Types of turbomachines. Turbomachines in which

Work is done by fluid

Work is done on fluid

Axial flow hydraulic turbine

Centrifugal pump

Radial flow hydraulic turbine

Axial flow pump

Mixed flow hydraulic turbine

Centrifugal compressor

Axial flow gas turbine

Axial flow compressor

Pelton wheel hydraulic turbine

Radial flow fan

One of two classes depending on whether work is done by the fluid on the rotating member or whether work is done by the rotating member on the fluid. Types of turbomachines can also be defined as to the manner of fluid movement through the rotating member. If the flow is essentially axial with no radial movement of the streamlines, then the machine is classed as an axial flow machine; whereas if the flow is essentially radial, it is classed as a radial flow or centrifugal machine. Considering the two classes of machines listed in Table (1.1) some broad generalizations may be made. The first is that the left-hand column consists of machines in which the fluid pressure or head (in (2)

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INTRODUCTION

the case of a hydraulic machine) or the enthalpy (in the case of a compressible flow machine) decreases from inlet to outlet, whereas in the right-hand column are listed those machines which increase the head or enthalpy of the fluid flowing through them. This decrease or increase in head, when multiplied by the weight flow per unit time of fluid through the machine, represents the energy absorbed by or extracted from the rotating blades, which are fixed onto a shaft. The energy transfer is affected in both cases by changing the angular momentum of the fluid. It might therefore be reasonable to assume that different types of turbomachine would exhibit differing shapes of blades and rotating members, In addition, because turbomachines have developed historically at different times, names have been given to certain parts of the machines as well as to different types of machines. And these are now defined. Turbine. A machine that produces power by expanding a continuously flowing fluid to a lower pressure or head; the power output is usually expressed in kW. Pump A machine that increases the pressure or head of a flowing liquid, and which is usually expressed in kPa or m. Fan a term used for machines imparting only a small pressure rise to a continuously flowing gas, usually with a pressure ratio across the machine of less than 1.15 such that the gas may be considered incompressible; pressure increase is usually expressed in mm of water. (3)

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INTRODUCTION

Compressor a machine imparting a large pressure rise to a continuously flowing gas with a pressure ratio in excess of 1.15. Impeller the rotating member in a centrifugal pump or centrifugal compressor. Runner the rotating member of a radial flow hydraulic turbine or pump. Rotor the rotating member of an axial flow gas or steam turbine; sometimes called a disc. Diffuser a passage that increases in cross-sectional urea in the direction of fluid flow and converts kinetic energy into static pressure head; it is usually situated at the outlet of a compressor. Draught tube a diffuser situated at the outlet of a hydraulic turbine. Volute a spiral passage for the collection of the diffused fluid of a compressor or pump; in the hydraulic turbine the volute serves to increase the velocity of the fluid before entry to the runner.

1.2 DIMENSIONAL ANALYSIS Many numbers of variables involved in describing the performance characteristics of a turbomachine virtually demands the use of dimensionless analysis to reduce the variables to a number of manageable dimensional groups. Dimensional analysis also has two other important uses: firstly, the prediction of a prototype performance from tests conducted on a scale model; and secondly, the determination of the most suitable type of machine on the basis of (4)

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INTRODUCTION

maximum efficiency for a specified range of head, speed and flow rate. Only a brief description of the method used for forming dimensionless groups and their application to model testing for turbomachines will be given here. Many hydraulic machines are so large that only a single unit might be required, as for example a hydraulic turbine in a hydroelectric installation producing many megawatts (MW) of power. Therefore, before the full-size machine is built, it is necessary to test it in model form to obtain as much information as possible about its characteristics. So that we may accurately transpose the results obtained from the model to the full-size machine, three criteria must be met. The first is that the model and prototype must be geometrically similar, that is, the ratio of all corresponding lengths between the model and prototype must be the same. The second requirement is that of kinematics similarity, where the velocities of the fluid particles at corresponding points in the model and prototype must be related through a fixed ratio. The third requirement is that of dynamic similarity, where the forces acting at corresponding points must be in a fixed ratio between model and prototype. For a geometrically similar model, dynamic similarity implies kinematics similarity.

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INTRODUCTION

1.2.1 Hydraulic Machines Figure (1.1) shows a control volume through which an incompressible fluid of density ρ flows at a volume flow rate of Q., which is determined by a valve opening. The head difference across the control volume is H.

P

Q

Speed N;(rpm) Flow rate; Q (m3/5)

N

Power; P (W)

gH

N

Energy difference across turbine; gH (N m/kg) Fluid density; ρ (kg/m3) Fluid viscosity; µ (Pa.s) Q

Diameter; D (m)

Figure 1.1 Hydraulic turbine control volume

and if the control volume represents a turbine of diameter D. which develops a shaft power P at a seed of rotation N, then we could say that the power output is a function of all the other variables, or P= f (µ,ρ,N,D,Q,(gH))………………..(1.1) in Eq. (1.1) f means ‘a function of’ and g the acceleration due to gravity has been combined with H to form the energy per unit mass of flow instead of energy per unit weight. We now assume that Eq. (1.1) may be written as the product of all the variables raised to a power and a constant, such that c a P =const[ ρ Nb µ Dd Qe(gH)f ]…….(1.2)

If each variable is expressed in terms of its fundamental (6)

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INTRODUCTION

dimensions, mass M. length L and time T. then, for dimensional homogeneity, each side of Eq. (l.2) must have the same powers of the fundamental dimensions, so the indices of M,L and T can be equated to form a series of simultaneous equations. Thus (ML2/T3) = const[(M /L3)a (1/T)b(M/LT)c (L)d’(L3 /T)e(L2/T2)f ]… (1 .3)

and equating the indices we get

M

1=a + c

L

2 = -3a- c + d +3e –2f

T

-3=-b-c-e-2f

There are six variables and only three equations. It is therefore possible to solve for three of the indices in terms of the remaining three. Solving for a,b and d in terms of c,e and f we get a=1-c b=3-c-e-2f d=5-2c-3e-2f Substituting for a,b and d in Eq. (1.2), P = const[ ρ

1− c

N 3 − c − e − 2 f µ c D 5 − 2 c − 3 e − 2 f Q e ( gH ) f ]

and collecting like indices into separate brackets. P = const[ ( ρN 3D5 )(µ / ρND2 )c (Q / ND3 )e ( gH / N 2D2 ) f ]...(1.4) The second term in the brackets will be recognized as the inverse of the Reynolds number and. since the value of is unknown, this term can be inverted and Eq. (1.4) may be written as P/ ρ N3D5 = const[{ ( µ / ρND 2 )c (Q / ND 3 ) e ( gH / N 2 D 2 ) f }-1]…(1.5) (7)

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INTRODUCTION

Each group of variables in Eq. (1.5) is truly dimensionless and all are used in hydraulic turbomachinery practice. Because of their frequent use, the groups are known by the following names: P/ ρ N 3 D 5 = P

the power coefficient

Q/ND3 = φ

the flow coefficient

gH/N2 D2 = ψ

the head coefficient

The term( ρ ND

2

/ µ )is

equivalent to the Reynolds number

(Re = ρ VD/ µ ), since the peripheral velocity V is proportional to ND. Hence, Eq. (1. 1) may be rewritten as

P =f (Re, φ ,ψ )……….(1.6) which states that the power coefficient of a hydraulic machine is a function of Reynolds number, flow coefficient and head coefficient. It is not possible to say what the functional relationship is at this stage. since it must be obtained by experiment on a particular prototype machine or model. In the case of a hydraulic machine, it is found that the Reynolds number is usually very high and therefore the viscous action of the fluid has very little effect on the power output of the machine and the power coefficient remain only a function of ψ and

φ . To see how P could vary with φ and ψ .

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INTRODUCTION

1.2.2 Compressible Flow Machines Not all turbomachines use a liquid (hydraulic fluid) as their fluid medium. Gas turbines and axial flow compressors are used extensively in the jet engines of aircraft where the products of combustion and air respectively are the working fluids, while many diesel engines use centrifugal compressors for supercharging. To accommodate the compressibility of these types of fluids (gases), some new variables must be added to those already mentioned in the case of hydraulic machines, and changes must be made in some of the definitions used.

T T

p01

p02

02 01

02s (a)

02s

p02

02

p01

01

s

(b)

s

Figure 1.2 Compression and expansion in compressible flow machines a) Turbine: b) compressor

With compressible flow machines, the parameters of importance are the pressure and temperature increase of the gas in a compressor and the pressure and temperature decrease of the gas in the turbine plotted as a function of the mass flow rate of the gas. In Fig, (1.2) the T-s charts for a compression and expansion process are shown. In isentropic flow the outlet, conditions of the gas are at 02s whereas (9)

CHAPTER 1

INTRODUCTION

the actual outlet conditions are at 02. The subscript 0 refers to total conditions and 1 and 2 refer to the inlet and outlet points of the gas respectively. The s refers to constant entropy. Now the pressure at the outlet P02 can be written as a function of the following variables: P02=f (D,N,m,p01,T01,T02, ρ01, ρ02,µ)….(1.7) Here the pressure ratio P02/ P01 replaces the head H in the hydraulic machine, while the mass flow rate m [kg/s] replaces Q. However, by examining Eq. (1.7) we can see that, using the equation of state. the density may be written as P =ρ /RT and it therefore becomes superfluous since we already have T and P as variables, so deleting density, and combining R with T, the functional relationship can be written as: P02=f(P01,RT01,RT02,m,N,D, µ ) and writing P02 as a product of the terms raised to powers. P02=f((P01)a (RT01)b (RT02)c (m)d (N)e (D)f( µ )g)

Putting in the basic dimensions M /LT2 = const[(M/ LT2)a (L2/T2 )b (L2/T2 )c (M/T)d (1/T)e (L)f (M/LT)g ]…(1.8)

Equating indices M

1=a+d+g

L

-1=-a+2b+2c+f-g

T

-2=-2a-2b-2c-d-e-g

and solving for a,b and f in terms of d, c, e and g we obtain (10)

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INTRODUCTION

a=1-d-g b=d/2-c-e/2+g/2 f=e-2d-g Substitute for a, b and f in Eq(1.8) then 1− d − g

P02=const[ P01

( RT01 ) d / 2−c −e / 2+ g / 2 ( RT02 ) c m d N e D e−2 d − g µ g ]

=const × P01{(RT02 / RT01) [m(RT01) c

1/ 2

/ P01D2 ]d [ND/(RT01)1/ 2 ]e[µ(RT01)1/ 2 / P01D]g} ...(1.9)

Now if the last term in the brackets in Eq. (1.9) is multiplied top and bottom by (RT01)1/2 and noting that P01 /RT01 equals ρ 01 then

µRT01 / P01(RT01)1/ 2 D = µ /(RT01)1/ 2 ρ01D But the unit of (RT01)1/2are L/Twitch is a velocity, and therefore the last term in brackets is expressible as a Reynolds number. Thus, the functional relationship may be written as

P02 / P01 = f ((RT02 / RT01),(m(RT01)1/ 2 / P01D2 ),(ND/(RT01)1/ 2 ), Re)….(1.10) The exact form of the function (1.10) must be obtained by experimental measurement taken from model or prototype tests. The Reynolds number is in most cases so high and the flow so turbulent that changes in this parameter over the usual operation range may be neglected. However, where large changes of density take place, a significant reduction in Re can occur and this must then be taken into account .For a particular constant diameter machine, the diameter D may be ignored and therefore, in view of the above consideration, function (1.10) becomes: (11)

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INTRODUCTION

P02 / P01 = f ((T02 /T01),(mT01 / P01),(N/T01 ))…. (1.11) 1/2

1/2

Where it should be noted that some of the terms are now no longer dimensionless.

1.3 parameters affecting the performance of hydraulic machine

1.3.1Effect of Speed Variation Consider a pump of fixed diameter pumping liquid with zero static lift. If the characteristic at one speed N1 is known, then it is possible to predict the corresponding characteristic at speed N2 and also the corresponding operating points. Fig. 1.3 shows the characteristic at speed N1, For points A, B and C the corresponding head and flows at a new speed N2. are found thus. We have

φ1 = φ 2

And Q1 N1 = Q2 N2 since D is constant …(1.12) Similarly

ψ

1

=ψ

2

And H1/N12=H2/N22 ……(1.13) Applying equations (2.55) and (2.56) to points A, B and C and letting the corresponding points be A\, B\ and C\. Q2 =Q1N2/N1 and H2 = H1(N2)2/(N1)2 (12)

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INTRODUCTION

or H2 α Q22 ……(1.14) and we see that all corresponding H

points lie on a parabola passing

N1

c

N2

throughthe origin. This means

A

B\ A\

at speed N1. it is only necessary to apply the similarity laws

B

c\

that for an operating point at A

System resistance

Hs

directly to find the corresponding

Figure 1.3

Q

operating point at the new speed since it will lie on the parabolic curve itself. However, if there is static 1ift (Hs ≠ 0) it will be necessary to calculate and then plot the corresponding points A\, B\ and C\ at the new speed, since the system curve will no longer pass through the origin. The system curve is then drawn to find the new operating point at its intersection with the N2 characteristic such that the corresponding maximum efficiency at design point DP2 remains the same as DP1 but at a different head and flow rate as in Fig.1.3

1.3.2Variation of Pump Diameter A variation of pump diameter may be similarly examined through the similarity laws. For a constant speed, Q1/D13 = Q2 /D23 and H1/ D12=H2/D22 (13)

CHAPTER 1

INTRODUCTION

or H α Q2/3 ……( 1.15) This curve does not lie on the system characteristic and therefore part of the new characteristic must be drawn through A\, B\ and C\ at the new diameter so that the new operating point may be found. The efficiency curve moves across in a similar manner to before, the corresponding efficiencies being equal. 1.4 CLASSIFICATION OF HYDRUALIC PUMPS AND COMPRESSORS The term ‘hydraulics’ is defined as the science of the conveyance of liquids through pipes. Most of the theory applicable to hydraulic pumps has been derived using water as the fluid medium but this by no means precludes the use of other liquids. Two types of pumps commonly used are centrifugal and axial flow types, so named because of the general nature of the fluid flow through the impeller. Both work on the principle that the energy of the

Figure (1.4) liquid is increased by imparting tangential acceleration to it as it flows through the pump. This energy is supplied by the flows through the

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INTRODUCTION

impeller, which in turn is driven by an electric motor or some other drive. In order to impart tangential acceleration to the liquid, rows of curved vanes or blades move transversely through it and the liquid is pushed sideways as it moves over the vanes as well as retainig its original forward component of velocity Figure (1.4) showed typical centrifugal and axial flow pump impellers, while between these two extremes lie mixed flow pumps, which are a combination of centrifugal and axial flow pumps, part of the liquid flow in the impeller being axial and part radial.

1.4.1CENTRIFUGAL PUMPS Figure (1.5) shows the three important parts of a centrifugal pump: 1) The impeller 2) The volute casing 3) The diffuser ring The diffuser is optional and may or may not be present in a particular design depending upon the size and cost of the pump. The impeller is a rotating solid disc with curved blades standing out vertically from the face of the disc. The tips of the blades are sometimes covered by another flat disc to give shrouded blades; otherwise the blade tips are left open and the casing of the pump itself forms the solid outer wall of the blade passages. The advantage of the shrouded blade is that flow is prevented from leaking across blade taps from one passage to

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INTRODUCTION

another.

Figure (1.5) Centrifugal pump and its component As the impeller rotates, the fluid that is drawn into the blade passages at the impeller inlet or eye is accelerated as it is forced radially outwards. In this way, the static pressure at the outer radius is much higher than at the eye inlet radius. The fluid has a very high velocity at the outer radius of the impeller, and, to recover this kinetic energy by changing it into pressure energy, diffuser blades mounted on a diffuser ring may be used. The stationary blade passages so formed have an increasing cross-sectional area as the fluid moves through them, the kinetic energy of the fluid being reduced while the pressure energy is further increased.

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INTRODUCTION

Vaneless diffuser passages may also be utilized. Finally, the fluid moves from the diffuser blades into the volute casing, which collects it and conveys it to the pump outlet. Sometimes only the volute casing exists without the diffuser however; some pressure recovery will take place in the volute casing alone.

1.4.2 AXIAL FLOW PUMPS

Figure (1.6) An axial flow pump consists of a propeller type of impeller running in a casing with fine clearances between the blade tips and the casing walls. In the absence of secondary flows, fluid particles do not change radius as they move through the pump; however, a considerable amount of swirl in the tangential direction will result unless means are provided to eliminate the swirl on the outlet side. This is usually done by fitting outlet guide vanes. The flow area is the same at inlet and outlet and the maximum head for this type of pump is of the order of

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INTRODUCTION

20 m. The usual number of blades lies between two and eight, with a hub diameter, impeller diameter ratio of (0.3-0.6). In many cases, the blade pitch is fixed but most large hydroelectric units have variable pitch blades to allow for load variations.

1.4.3 DISPLACEMENT PUMPS 1.4.3.1 GENERAL CONSIDERATIONS The method of transforming the mechanical energy of a prime mover into the energy of fluid flow in positive displacement pumps is basically different from energy conversion in rotodynamnic pumps. In a displacement pump the hydraulic fluid is delivered in intermittent “characteristic volumes’’ or portion by suitably designed pumping elements. The pumping elements, whatever their design, serve to effectively seal off the intake, suction side of the pump from the outlet, pressure, side in order to prevent leakage and backflow of the hydraulic fluid. Thus, the delivery of a displacement pump generally fluctuates more or less and the mean delivery over a certain period of time is commonly considered. The principle of positive displacement pump operation enables the following expression to be written for the theoretical, or ideal, mean delivery per second :

Q

t

=

wzn 60

=

Wn [m 60

3

].........

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..........

...( 1 . 16 )

CHAPTER 1

INTRODUCTION

Where

w = Displacement (i.e., characteristic volume delivered per revolution of pump shaft) of each pumping element; z = number of pumping elements (i.e., number of characteristic volumes delivered per revolution); W = pump displacement (i.e., theoretical (delivery per revolution). By theoretical delivery is understood the delivery of an incompressible fluid by a pump operating without leakage or cavitation. According to the manner in which the hydraulic fluid is pumped, positive- displacement pumps are subdivide into reciprocating and a rotary pumps. A reciprocating pump is a positive-displacement machine which delivers pressure by linear reciprocating motion of the pumping elements. The motion of the pumping elements is most commonly effected by means of a crankshaft mechanism, though camshaft, eccentric and other drives are frequently employed. Classified with reciprocating pumps are also plungers, diaphragm and other pumps having a similar process of fluid ejection. All reciprocating pumps are provided with intake and outlet valves to regulate fluid flow through the working chamber. The valves usually operate automatically, the degree of opening being governed solely by the force developed by the working fluid.

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INTRODUCTION

Reciprocating pumps are capable of developing very high pressures, running into tens and hundreds of atmospheres, but they operate at a rotative speed of the prime mover of no more than 250 to 500 rpm. That is why a reciprocating pump is always much bigger than a centrifugal pump or equal capacity. Powerful mechanically driven reciprocating pumps are employed in the oil and chemical industries for pumping viscous fluids and at thermal electric stations for feeding steam boilers. Small hand-operated pumps are used in a wide range of applications. In water supply systems and other fields reciprocating pumps are being replaced by centrifugal and rotary pumps. A rotary pump is a positive-displacement pump which delivers pressure by a pure rotation or a combined rotation and oscillation of the pumping elements. Any rotary pump consists basically of a stationary housing in which is nested a power-driven rotor carrying one or more pumping elements. A variety of rotor and pumping element designs have been developed, some of which will be described further on. The principle of rotary pump operation is as follows: the hydraulic in fluid entering the inlet port is trapped by the pumping elements which carry it around to the outlet port, where it is expelled under pressure into the delivery pipeline.

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INTRODUCTION

Rotary pumps need no intake or outlet valves, a feature, which makes them reversible, i.e., they can work ether as pumps or as motor. Furthermore, they do not require a crankshaft mechanism, which enables them to be operated at very high rotative speeds, up to 5,000 rpm and more. The theoretical delivery of a rotary pump is also determined by equation. (1.16). The number of pumping elements and consequently of characteristic volumes delivered per revolution, however, is greater than in reciprocating pumps (z= 4-l2 and more, as compared with z=13 in reciprocating pumps). Besides, in rotary pumps delivery of characteristic volumes overlaps, i.e., the hydraulic fluid is drawn in at the in take port before an adjacent volume has been expelled at the outlet port. This accounts for greater uniformity of delivery than in reciprocating pumps. Those advantages of rotary pumps have gained them numerous applications in many fields, including aviation. In aircraft systems rotary pumps are used in engine fuel and lubricating systems and in hydraulic power transmission. 1.4.3.2 TYPES OF ROTARY PUMPS Rotary pumps are classified into three main types: Gear pumps; which may be of the spur-gear or screw type. Spur-gear pumps deliver the hydraulic fluid at right angles to the rotation Figure (1.7) (21)

CHAPTER 1

INTRODUCTION

axis of the pumping elements; the screw pump delivers the fluid along the lie rotation axis. Van pumps, in which the hydraulic fluid is trapped in spaces between the pump housing, rotor and vanes. Gear pump, Piston pumps, radial or axial, in which, the fluid is trapped in cylinder bores in the rotor. Gear pumps (Fig. 1.7) are most commonly constructed with a pair of identical spur gear with involute teeth revolving in a closely fitted housing. The oil coming in at the intake port fills the spaces between the teeth and is carried around the periphery of the revolving gears to the discharge side. The teeth are meshing between the two gears and thus prevent the return of oil from the discharge to the suction. However, as the spaces between the teeth are larger than the teeth, some oil is carried back to the low-pressure side. The characteristic volume, therefore, is not the volume of a space but the volume of a tooth wtooth. The number of such volumes delivered per revolution equals the number of teeth of the two gears (2z). Hence the theoretical displacement of a gear pump is Qt=2zwtoothn/60 [m3/s]……(1.17) where n is a number of teeth. A screw pump operates on the same principle but its kinematics is three-dimensional. Despite such substantial advantages as completely

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CHAPTER 1

INTRODUCTION

uniform delivery and high speed operation screw pumps have not yet found wide application in aeronautical engineering. Vane pumps most commonly used in aircraft, hydraulic systems have four vanes and the flow is two-dimensional .The rotor represent a hollow cylinder with radial slots in which the vanes slide. The rotor is placed eccentrically in relation to the cylindrical housing thanks to which the vanes slide back and forth, as it revolves. Centrifugal force keeps the vanes tips in contact with the track ring. The inner tips slide around a so-called floating axle without bearings. When the rotor turns the fluid is drawn in on one side as the spaces formed between the housing, vanes and rotor increase to the characteristic volume w, and is forced out on the pressure side as they decrease. Rotary piston pumps may have either two-dimensional or three-dimensional flow characteristics. To the former belong radial-piston pumps in which an eccentric rotor, called the cylinder-barrel or block, caries a number of cylinders in which pistons oscillate when the motor turns the piston tips

Figure (1.8) (23)

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INTRODUCTION

(sometimes made with rollers) slide along a track ring in the housing. The rotation of the cylinder block periodically connects the cylinders through small bores in their bottoms with the suction and discharge ports in the center separated by a dividing wall the pistons draw in oil as they pass around the intake side and expel it at the outlet side. The characteristic volume of a piston pump is the volume traveled through by each piston in one stroke;

w=

where d=piston diameter;

πd 2 4

2e ……(1.18)

e=eccentricity. The theoretical mean displacement for z piston is

Qt =

π d 2 ezn 120

…(1.19)

1.5 PUMP AND SYSTEM MATCHING It has been shown that a hydraulic pump has a design point at which the overall efficiency of operation is a maximum. However, it may happen that the pipe system in which the pump is being used is unsuited to the pump and a different pump with a more suitable characteristic is required. This section will examine how a pump and a pipe system may be matched to each other. Consider the pipe system in Fig (1.9). On the suction side

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CHAPTER 1

INTRODUCTION

the losses expressed in terms of standard loss coefficients are the sum of the minor losses hin hin=ΣkVi2/2g……(1.20) Hd

and the friction loss hfi= 4fli Vi2/2gdi……(1.21)

Hs Pump

Where f is the Darcy friction factor, Hs

li is the length of the inlet pipe and di its diameter.

Figure (1.9)

Thus the total head loss is

hi=4fli Vi2/2gdi+ΣkVi2/2g……(1.22) On the delivery side the sum of the bend, friction and exit losses that must be overcome is ho=4flo Vo2/2gdo+ΣkVo2/2g……(1.23) Finally, the liquid must be moved from the lower reservoir to the upper reservoir through the static head Hs hence the total opposing head of the pipe system that must be overcome in order to move the fluid from the lower to upper reservoir is H=Hs+ho+hi…(1.24) Now from the continuity equation the flow rate through the system is proportional to the velocity. Thus the resistance to flow in the form of friction losses, head losses, etc., is proportional to the square of the flow rate and is usually written as System resistance = KQ2

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INTRODUCTION

It is a measure of the head lost for any particular flow rate through the system. If any parameter in the system is changed, such as adjusting a valve opening, or inserting a new bend, etc., then K will change. The total system head loss therefore becomes H=Hs+KQ2……(1.25) and if this equation is plotted on the head-flow characteristic, the point at which equation (1.25) intersects the pump characteristic is the operating point, and this may or may not lie at the Efficiency, Head Efficiency

Design point

Operating Point Head

H=Hs+KQ2

Hs

Q

Figure 1.10 duty point, which usually corresponds to the design point and maximum efficiency. The closeness of the operating and dutypoints depends on how good an estimate of the expected system losses has been made. In Fig. (1.10) the system curve is superimposed on the HQ characteristic. It should be noted that if there is no static head rise of the liquid (e.g. pumping in a horizontal pipeline between two

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CHAPTER 1

INTRODUCTION

reservoirs at the same elevation) then Hs is zero and the system curve passes through the origin. This has implications when speed and diameter changes take place. Because of the flatness of rotodynamic pump characteristics, a poor estimate of the system losses can seriously affect the flow rate and head; whereas in positive displacement pumps. the H-Q curve is almost vertical and, even if the head changes substantially, the flow rate stays almost constant.

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CHAPTER 2

MEASUREMENTS

CHAPTER 2

MEASUREMENTS 2.1 Measurements Measurements provide us with a mean of describing various phenomena in quantitative terms.

2.2 Mechanical Measurements The measurements involved in the field of mechanical engineering are classified into two broad categories: i)

Mechanical type, and

ii)

Power type

2.2.1 Mechanical type Measurements Mechanical type of measurements are used as a design tool for experimental, and research and developmental programs. 2.2.2 Power type measurements There has always been a strong link between measurement and control. Power types of measurements are monitoring or operational measurements, which are usually a part of control system.

2.3 Method of Measurements The method of measurement may be classified into two categories. 2.3.1 Direct Method In this method the unknown quantity is directly compared against a standard. The result is expressed as a numerical number and (28)

CHAPTER 2

MEASUREMENTS

a unit. 2.3.2 Indirect Method Measurements by direct methods are not always possible, feasible and practicable. These methods in most of the cases , are inaccurate because they involve human factors. They are also less sensitive. Hence direct methods are not preferred and are rarely used. In engineering application, Measurement Systems are used. These measurement systems use indirect method for measurement purposes. A measurement system consists of a transducing element, which converts the quantity to be measured into analogous signal. The analogous signal is then processed by some intermediate means and is then fed to the end devices, which present the result of measurement. Power transmitter (shaft)

Power sink

Power source

Cradled source

(b)

(a) F

Transmitted torque sensor

F Cradled sink

(d)

(c)

Figure (2.1)

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MEASUREMENTS

2.4 Torque Measurement on Rotating Shafts Measurement of the torque carried by a rotating shaft is of considerable interest for its own sake and also as a necessary part of shaft power measurements. Torque transmission through a rotating shaft generally involves both a source of power and a sink (power absorber or dissipator), as in Figure. (2.1). Torque measurement may be accomplished by mounting either the source or the sink in bearings (“cradling”) and measuring the reaction force F and arm length L, or the torque in the shaft itself is measured in terms of the angular twist or strain of the shaft (or a torque sensor coupled into the shaft). The cradling concept is the basis of most shaft power dynamometers. These are used mainly for measurements of steady power and torque, using pendulum or platform scales to measure F. Gages 2 and 3 also at 45o with shaft axis

Figure (2.2) The use of elastic deflection of the transmitting member for torque measurement may be accomplished by measuring either a gross motion or a unit strain. The strain-gage bridge configuration generally used to measure torque is shown in figure (2.2). This arrangement (assuming accurate gage placement and matched gage characteristics) (30)

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MEASUREMENTS

is temperature-compensated and insensitive to bending or axial stresses. The gages must be precisely at 45o with the shaft axis, Placement of the gages on a square, rather than round, cross section of the shaft has some advantages. The gages are more easily and accurately located and more firmly bonded on a flat surface. In either case, a main difficulty is the necessity of being able to read the deflection while the shaft is rotating. Figure (2.3) illustrates a torsionbar torquemeter using optical methods of deflection measurement. The relative angular displacement of the two sections of the torsion bar can be read from the calibrated scales because of the stroboscopic effect of intermittent viewing and the persistence of vision. Observer

mirror Light source T Torsion bar T

Figure (2.3) The desire for electrical output signals and for the ability to measure rapidly varying torque has led to the development of straingage torque-meters. The problem of getting bridge power onto the shaft and output signals off the shaft has a number of possible solutions. If rotation is slow and the total angle turned through is (31)

CHAPTER 2

MEASUREMENTS

small, one may simply let the connecting wires wrap around the shaft. For continuous rotation, slip rings and brushes may be used. The torque of many machines, such as reciprocating engines, is not smooth even when the machine is running under “steady-state” conditions. If one wishes to measure the average torque so as to calculate power, the higher frequency response of strain-gage torque pickups may be somewhat of a liability since the output voltage will follow the cyclic pulsations and some sort of averaging process must be performed to obtain average torque.

2.5 Speed Measurement on Rotating Shafts 2.5.1 D.C tachometer generator for rotary velocity measurement An ordinary d-c generator (using either a permanent magnet or separately excited filed) produce an output voltage roughly proportional to speed .By emphasizing certain aspect of design, such a device can be made an accurate instrument for measuring speed rather than a machine for producing power.

2.5.2 A-C tachometer generators for rotary-velocity measurement An a-c two-phase squirrel-cage induction motor can be used as a tachometer by exciting one phase with its usual a-c voltage and taking the voltage appearing at the second phase as output. With the rotor stationary, the output voltage is essentially zero. Rotation in one direction causes at the output an a-c voltage of the same frequency as (32)

CHAPTER 2

MEASUREMENTS

the excitation and of amplitude proportional to the instantaneous speed. This output voltage is in phase with the excitation. Reversal of rotation causes the same action except the phase of the output shifts 180o. 2.5.3 Eddy-current drag-cup tachometer Figure (2.4) shows schematically an eddy-current tachometer. Rotation of the magnet induces voltages into the cup, which thereby produce circulating eddy currents in the cup material. These eddy currents interact with the magnet field to produce a torque on the cup in proportion to the relative velocity of magnet and cup. This causes the cup to turn through an angle θο until the linear spring torque just balances the magnetic torque. Thus in steady state the angle θo is directly proportional to the input velocity.

spring

Conducting and nonmagnetic cup Permanent magnet

Figure (2.4)

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MEASUREMENTS

2.6 Shaft Power Measurement (Dynamometers) The accurate measurement of the shaft power input or output of power-generating, transmitting, and absorbing machinery is of considerable interest. While the basic measurements, torque and speed, have already been discussed, their practical application to power measurement will be considered briefly here. The term dynamometer is generally used to describe such power-measuring systems although it is also used as a name for elastic force sensors. The type of dynamometer employed depends somewhat on the nature of the machine to be tested. If the machine is a power generator, the dynamometer must be capable of absorbing its power. Test object

Dynamometer

Tachometer generator Load cell

Figure (2.5) (34)

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MEASUREMENTS

If the machine is a power absorber, the dynamometer must be capable of driving it. If the machine is a power transmitter or transformer, the dynamometer must provide both the power source and the load. In all power-measurement applications torque and speed are separately measured and then power is manually calculated. This calculation can be performed automatically in a number of ways since the basic operation (multiplication) can be accomplished physically in various ways. An interesting scheme using the properties of bridge circuits is shown in Figure (2.5). Speed is measured with a d-c tachometer generator, and this voltage is applied as the excitation of a strain-gage load cell used to measure torque. Since bridge output is directly proportional to excitation voltage and also directly proportional to torque, the voltage e0 is actually an instantaneous power signal.

2.7 Pressure Measurement 2.7.1 Basic Methods of Pressure Measurement Since pressure can usually be easily transduced to force by allowing it to act on a known area, the basic methods of measuring force and pressure are essentially the same, except for the highvacuum region where a variety of special methods not directly related to force measurement are necessary.

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MEASUREMENTS

2.4.2 Manometers The manometer, in its various forms, is closely related to the piston gage since both are based on the comparison of the unknown pressure force with the gravity force on a known mass. The manometer differs, however, in that it is self-balancing, is a deflection rather than a null instrument, and has continuous rather than stepwise output. The accuracies of dead-weight gages and manometers of similar ranges are quite comparable; however, manometers become unwieldy at high pressures because of the long liquid columns involved. The U-tube manometer of Figure (2.6) is usually considered the basic form and has the following relation between input P2

and output for static conditions: h=(P1-P2)/ρ g

h P1

where g : gravity acceleration.

ρ : mass density of manometer fluid.

Figure (2.6)

If P2 is atmospheric pressure, then h is a direct measure of P1, as a

Inclined manometer

Well type manometer

Barometer Micromanometer

Figure (2.7) (36)

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MEASUREMENTS

gage pressure. Note that the cross-sectional area of the tubing (even if not uniform) has no effect. A number of practically useful variations on the basic manometer principle are shown in Figure (2.7). The cistern or well-type manometer is widely used because of its convenience in requiring reading of only a single leg. The well area is made very large compared with the tube; thus the zero level moves very little when pressure is applied. Even this small error is compensated by suitably distorting the length scale. However, such an arrangement, unlike a U tube, is sensitive to nonuniformity of the tube cross-sectional area and is thus considered somewhat less accurate.

2.7.3 Elastic Transducers While a wide variety of flexible metallic elements might conceivably be used for pressure transducers, the vast majority of practical devices utilize one or another form of Bourdon tube, diaphragm, or bellows as their sensitive element, as shown in Figure (2.8). The gross deflection of these elements may directly actuate pointer-scale readout through suitable linkages or gears, or the motion may be transduced to an electrical signal by one means or another. The Bourdon tube is the basis of many mechanical pressure gages and is also widely used in electrical transducers by measuring the output displacement with potentiometers, differential transformers, etc. The basic element in all the various forms is a tube of noncircular cross section. A pressure difference between the inside and outside of the (37)

CHAPTER 2

MEASUREMENTS

Tube cross section

Bourdon tubes

Diaphragms

Bellows

Figure (2.8) tube (higher pressure inside) causes the tube to attempt to attain a circular cross section. This results in distortions, which lead to a curvilinear translation of the free end in the C type and spiral and helical types and an angular rotation in the twisted type, which motions are the output.

2.8 volume flow rate measurement The total flow rate through a duct or pipe must often be measured and/or controlled. Many instruments (flowmeters) have been developed for this purpose. They may be classified in various ways; a useful overall classification divides devices into those, which measure (38)

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MEASUREMENTS

volume flow rate (m3/time) and those, which measure mass flow rate (kg/time).

2.8.1 Constant-area, variable-pressure-drop meters Perhaps the most widely used flowmetering principle involves placing a fixed-area flow restriction of some type in the pipe or duct carrying the fluid. This flow restriction causes a pressure drop which Static pressure

Measured pressure drop

Permanent pressure loss

Differential pressure sensor

Sharp edge

Orifice plate Minimum flow area

Flange tape

Most widely used

2.5D

8D

Figure (2.9) (39)

CHAPTER 2

MEASUREMENTS

varies with flow rate; thus measurement of the pressure drop by means of a suitable differential pressure pickup allows flow-rate measurement. In this section we shall briefly discuss the most common practical devices that utilize this principle: the orifice, the flow nozzle and the venturi tube.

2.8.1.1 Orifice meter The sharp-edge orifice is undoubtedly the most widely used flowmetering element, mainly because of its simplicity, low cost, and the great volume of research data available for predicting its behavior. A typical flowmetering setup is shown in Figure (2.9). If onedimensional flow of an incompressible frictionless fluid without work, heat transfer, or elevation change is assumed, theory gives the volume flow rate Q (m3/s) as

Qt =

A2 f 1 − ( A2 f / A1 f ) 2

2( P1 − P2 )

ρ

We see that measurement of Q requires knowledge of A1f , A2f and ρ and measurement of the pressure differential (P1 — P2). Actually, the real situation deviates from the assumptions of the theoretical model sufficiently to require experimental correction factors if acceptable flowmetering accuracy is to be attained. For example, A1f and A2f are areas of the actual flow cross section, which are not, in general, the same as those corresponding to the pipe and orifice diameters, which are the ones susceptible to practical measurement. Furthermore, A1f and A2f may change with flow rate because of flow geometry changes. (40)

CHAPTER 2

MEASUREMENTS

Also, there are present frictional losses that affect the measured pressure drop and also lead to a permanent pressure loss. To take these factors into account, an experimental calibration to determine the actual flow rate Qa. A discharge coefficient Cd may then be defined by Cd=Qa/Qt and thus

Qa =

2( P1 − P2 )

C d A2 f 1 − ( A2 f / A1 f ) 2

ρ

The discharge coefficient of a given installation varies mainly with the Reynolds number Re at the orifice. Thus the calibration can be performed with a single fluid, such as water, and the results used for any other fluid as long as the Reynolds numbers are the same.

2.9 Components and System Accuracy We have discussed component tests, instrumentation, and test procedures it is important to review the overall picture once the test procedures and a schematic have been designed. Instrumentation accuracy is only the initial step in constructing an accurate test system. The minute characteristics of a component under test or a component within the test circuit may create test data that are inconsistent or totally inaccurate

2.9.1 General Accuracy Terms (41)

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MEASUREMENTS

Most instruments have ratings to define the various effects that cause deviation of accuracy. These ratings usually apply to instruments of different types, so this section will be devoted to explaining what these general terms mean. Any terms that apply specifically to one type of instrument will be discussed in the section pertaining to that instrument.

2.9.1.1 Accuracy of Reading An instrument with a rating of percentage of reading will maintain a constant deviation tolerance throughout the full range output. For example, a flowmeter with a range of 10-100 lit/min, which has an overall accuracy rating of ± 1 % of reading will have a deviation of ±1 lit/min at 100 lit/min and ± 0.1 lit/min at 10 lit/min.

2.9.1.2 Ambient Effects Ambient effects can apply to any external condition surrounding a transducer. The accuracy may be affected by temperature, pressure, and humidity. etc. Each transducer rating should be studied carefully if it is to be applied in a situation with variable ambient conditions.

2.9.1.3 Best Fit through Zero Best fit through zero defines the maximum deviations expected in a nonlinear out device. This includes the effects of nonlinearity, hysteresis and nonrepeatibility.

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MEASUREMENTS

2.9.1.4 Combined Error Combined error is the maximum deviation expected from more than one error-causing effect. Some transducers are rated in this manner to provide an easy method of predicting maximum error.

2.9.1.5 Compensation Compensation defines a method used to correct for an error-causing effect. Generally, a transducer can be mechanically designed to negate certain effects, or the electronics can allow correction for potential error. A transducer rating will normally describe a range that will be corrected automatically. Outside of this range the error causing effects will reduce accuracy.

2.9.1.6 Creep Creep is the change of transducer output over a period of time with all external and internal conditions remaining constant.

2.9.1.7 Creep Recovery Creep recovery is the time it takes for a transducer to return to its initial no load output after all loads have been removed. This term is usually expressed as a percentage of rated output.

2.9.1.8 Drift A change in transducer output with no change in load is called drift. Drift can apply to any characteristic. A common example is pressure (43)

CHAPTER 2

MEASUREMENTS

transducer zero drift. When power is applied to a transducer at no load, you will read one output value. After 5 or 10 mm, still at no load, you will read a different output. (Not all pressure transducers drift; however this is one area where the problem is common )

2.9.1.9 Frequency Response Frequency response is the range of frequencies that a transducer will follow the sinusoidally varying mechanical input within the specified limits. 2.9.1.10 Full-Scale Output An instrument with a rating that reads percentage of full-scale output will provide the same accuracy. To calculate the actual accuracy of a full-scale-accuracy instrument, you must first determine the maximum output of the device. The percentage accuracy rating is now applied to this maximum value. The resultant value applies to any point within the full range of the instrument. This is a common error found when a transducer is selected for a high-accuracy application. It is often assumed that ± 1 % means ± 1 % of reading, when in fact the error is much greater at lower output.

2.9.1.11 Hysteresis Hysteresis is the difference in transducer output between reading the same value when coming up to the value or going down to the measured value (i.e., increasing load reading versus decreasing load reading). (44)

CHAPTER 3

REGENERATIVE TURBINE PUMPS

CHAPTER 3


3.1 Why Regenerative turbine pump? Today, two main types of pump dominate the scene in the chemical process industries: positive-displacement pumps and impeller pumps. For pumping applications that involve highly volatile fluids, the choices are limited. When such fluids are allowed to flash to vapor during pumping, the eventual collapse of the entrained vapor bubbles will create cavitation that can severely damage pump internals. Unlike many other pump types, the regenerative turbine pump (a type of impeller pump) is becoming the preferred type of pump for situations in which transient cavitation conditions occur, such as during the handling of high-volatility fluids. The various attributes of regenerative turbine pumps are discussed below. Pump primer In all positive-displacement pumps (either reciprocating or rotary), the action of the pump alternately fills and then empties one or more cavities with the pumped fluid. Fluid is pushed into a created volume, by both the pressure on the free surface of the inlet fluid and the static head above the inlet. With the appropriate valving, the destruction of this created volume then

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pushes the fluid out against whatever pressure exists at the outlet.

Figure(3.1) By comparison, the impeller pump imparts kinetic energy to the fluid, which is borne as potential energy or pressure. In general, positive-displacement pumps attempt to maintain a

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CHAPTER 3


given flow rate regardless of required pressure, while impeller pumps attempt to maintain pressure regardless of flow. Within each pump category, many subtypes have been developed to improve pump performance for different types of fluids. For instance, the most popular impeller pump is the centrifugal pump, with its curved vanes, while the regenerative turbine pump, shown in Figure(3.1), is another lesser-known variation. Overall, the impeller pump family includes several “turbine” pumps. These include the horizontal-shaft diffuser pump, and the vertical-shaft deep-well centrifugal pump. Turbine pumps can also be subcategorized as vortex, periphery or regenerative turbine pumps, based on the shape of the blades that impart energy to the liquid, and the direction of the liquid as it leaves the blade. All centrifugal pumps take liquid in at the center of the impeller. Some push it radially outward, with no axial component to the velocity. The propeller moves the liquid along the axis of the drive shaft, and imparts no radial component to the velocity of the pumped fluid. By comparison, mixed-flow pumps are often called turbine pumps, because their impellers (part axial and part centrifugal in design and function) move the liquid outward from the center. These impellers impart both a radial and an axial component to the fluid flow.

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In all these pump types, the liquid passes through the impeller only once, and thus has all the energy added in a single pass through the pump blades. By comparison, in a regenerative turbine pump, the liquid is exposed to the impeller many times, with additional energy being imparted to the fluid each time it passes through the blades, allowing substantially more motive force to be added. This allows for much higher pressures to be achieved in a more-compact pump design. In fact, of all the centrifugal pump types that this author is familar with, the regenerative turbine pump is the only one in which the fluid passes the impeller blades more than once as it travels from inlet to outlet for a given impeller stage.

3.2 How regenerative pumps work?

Figure (3.3) Figure (3.2) A typical impeller and housing of a regenerative turbine pump are shown in Figure(3.1) . The fluid is in contact with the fluted portion of the impeller. The impeller, through centrifugal

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CHAPTER 3


forces, propels the fluid radially outward. The enclosing chambers conduct the fluid into twin vortices around the impeller blades, as shown in Figures (3.2) and (3.3). A small pressure rise occurs in the vicinity of each impeller blade. Vortices are formed on either side of the impeller vanes, with their helix axes curved and parallel to the circumference of the impeller. This is shown in Figure (3.3) To visualize the path the fluid follows in a regenerative turbine pump, imagine a spring that has been stretched too far, so that the coils no longer touch. Take that stretched spring, form it into a circle, and lay it on the impeller blade. As you follow the coiled spring, you would see the progression of movement from one blade to the trailing blade. Depending on how far the spring has been stretched (the distance between coils could be large relative to the coil diameter) the pitch of one loop may span more than the distance between adjacent blades. As the discharge pressure increases, the pitch of the loops in the helix gets smaller, in a manner analogous to compressing the spring. It has been visually confirmed that as the discharge pressure increases, the helical pitch of the fluid becomes shorter.

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3.3 Cavitation in Regenerative Turbine pump With this mental picture in mind, one of the most salient features of the regenerative turbine pump is pointed out. First, the vapor bubbles found in the incoming fluid, because of the inertia of the liquid in the vortex, are forced away from the metal walls of the pump into the center of the helix (spring). Second, the rate of pressure increase from inlet to outlet is much lower than for any other type of pump, because the pressure is building continuously around the pumping channel, rather than in a single quick passage through the blades. The shock of collapsing bubbles is virtually non-existent, and any bubbles that do collapse impinge on adjacent fluid, not on the metal pump components.

3.3.1 Preventing cavitation As mentioned earlier, in a centrifugal impeller pump, the fluid only passes through the centrifugal impeller once, so it only gains energy in that single pass. This is shown in the flat discharge head curve for the centrifugal unit shown in Figure (3.4). By comparison, a flow-pressure curve for a (4-in) regenerative turbine impeller, and that of a centrifugal impeller of (7.5-in) diameter., are compared in Figure (3.4) (note that similar flow rates are provided from the smaller regenerative turbine pump). The increase in pressure in the regenerative turbine is also responsible for the increase in power required.

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CHAPTER 3


As the fluid moves from the inlet area to the outlet, pressure continuously builds, with subsequent passes through the impeller channels adding energy to the vortex. This energy manifests itself as pressure. As the discharge flow is reduced, the time the fluid takes to move from inlet to outlet increases, and consequently, the fluid has more energy imparted to it. This additional buildup of pressure provides the ramped pressure curve seen in Figure (3.4). As mentioned, the fluid arriving at the discharge of a regenerative turbine impeller will have undergone a gradual pressure increase. By design, any entrained vapor bubbles occurring at the inlet will move to the center of the vortex (where the pressure is the lowest); here, they will collapse gently, over a relatively extended period of time, and generally away from the metal surfaces. This gentle collapse of the vapor bubbles occurs in a process similar to that in a condenser. By contrast, in the centrifugal impeller, the bubbles move rapidly from low to high pressure, and subsequently collapse violently. In the inlet of a regenerative turbine pump, the presence of vapor bubbles reduces flow but does not deteriorate the pump parts. This characteristic is reflected in the reduced flow that results when Net Positive Suction Head available (NPSHa) is reduced below the NPSH required (NPSHr). The regenerative turbine pump's ability to continue operation without damage in the presence of vapor bubbles is particularly advantageous when

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CHAPTER 3


transient events occur that cause inlet pressures to fall below normal levels.

3.3.2 Pumping volatile fluids Engineers know that volatile fluids are more difficult to move than ordinary ones. Volatile fluids (those that flash to vapor easily) often will not tolerate an absolute pressure that is low enough to permit effective pumping without requiring that the fluid-supply level be substantially higher than the pumping mechanism. While it is often desirable to maintain low pumping velocities in all fluids at low pressure, it is critical to maintain volatile fluids at a lower velocity in the suction inlet. The higher the velocity as the fluid enters either the internal passages in a positivedisplacement pump, or the impeller in a kinetic pump, the greater the inertia-induced pressure drop. As the liquid pressure drops, the liquid bursts into vapor, causing either partial or total vapor binding (a condition in which the pumping chamber fills with vapor), rather than with liquid. In the worst case, a balance of state (liquid-to-vapor) can be created, where the pressure created in the intake equals the vapor pressure of the liquid. Then, any liquid trying to enter the pumping volume is caused to boil, rather than move as a liquid. During the pumping of volatile fluids, any energy that accrues because of localized turbulence (i.e., as a result of

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CHAPTER 3


surface roughness or changes in direction in the line conduit) can add sufficient energy to vaporize the liquid in the pump. Even sunlight on the suction line piping can impart sufficient energy to cause volatile fluids to flash to vapor. In situations where the supply cannot be elevated many feet above the pump inlet, or when transient conditions, such as a sudden increase in pumping demand, occur and result in the loss of the elevated supply, both positive-displacement and centrifugal-type pumps experience cavitation, with its damaging consequences

3.4 Effect of increasing pumping flow rate on the performance When the pump speeds up to increase output, the fluid in the suction line has to speed up to compensate. This means that the fluid has to accelerate to the higher flow rate. The force to accelerate this mass of liquid is developed through the trade of pressure for velocity (Bernoulli's principle). Two primary attributes of regenerative turbine pumps merit consideration. First and foremost is their ability to tolerate cavitation in the inlet fluid. Second are the pressure-flow characteristics that typify this type of pump, as shown in Figure (3.4). When the element receiving the pump's flow has difficulty adjusting pressure, and reasonably consistent flow is desired, the ramped pressure curve that characterizes a regenerative turbine (53)

CHAPTER 3


pump can continue to deliver liquid at the desired flow rate, while a centrifugal pump could be completely shut down. The downside to this is the energy (in the form of heat) that is put into the fluid by running the pump with the discharge shut off.

Eff,%

H,f t

HP

Capacity,GPM

If regenerative turbine pump is throttled to reduce its output discharge ,pressure and power increase

Eff, %

H, ft

HP

Capacity, GPM

Power needed to derive a medium head centrifugal pump decreases as the discharge head increase as indicated by the horse power and head capacity curves

Figure (3.4) From www.rothpump.com

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CHAPTER 3


The resulting pressure may exceed the manufacturer's limits and damage the pump. Since pressure is the result of kinetic energy added to the liquid, it is obvious that there is much more energy going into the fluid pumped by the regenerative turbine pump than the fluid pumped by the centrifugal pump. Overall, the volume of liquid in a centrifugal pump is generally much higher than in a comparable turbine pump. With higher energy going into a smaller volume, the temperature of the liquid in the turbine pump will increase much faster when the pump discharge is blocked.

3.5 Pump specifications In specifying a regenerative turbine pump, as with most applications, the seal is a critical element to be determined. Care in selecting the type of seal (whether double, tandem, oil or gas), the barrier or buffer fluid or gas (to ensure compatibility with the fluid being pumped), the pumped fluid temperatures, and the material compatibility are essential. Some fluids require highly elevated temperatures to be pumpable (such as the use of customized seal designs) are required. Regenerative turbine pumps tend to have more internal components than do centrifugal pumps. The centrifugal impeller can be fabricated or cast (with the outside diameter machined). By comparison, the regenerative turbine impeller is completely

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CHAPTER 3


machined. The encasing flow chambers on each side of the impeller (Figure 3.2) are also machined on most surfaces. In general, the clearances are held to closer tolerances than are those on centrifugal pumps. Because of this, regenerative turbine pumps are sometimes more expensive than other pumps. However, the major factor to examine when selecting a system is the total cost of the system needed to move the target liquid. With conventional pumps, volatile fluids may require a higher tank to provide adequate NPSHa. Raising the tank will require longer support legs, and, if in a seismic area, a substantially stronger supporting structure in the lateral directions. Raising the reservoir may also require a higher ceiling or roof. All of these measures will incur additional costs. Overall, the ability to handle transient conditions that would otherwise cause significant cavitation without damage will add substantial life to the pump, which means much less downtime and fewer repair costs.

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CHAPTER 4

THEORETICAL ANALYSIS OF REGENERATIVE TURBINE PUMP

CHAPTER 4

Theoretical Analysis of Regenerative Turbine Pump 4.1 Introduction The regenerative turbine pump, as shown schematically in figure (4.1) consists of impeller and collecting passage. The impeller has pockets, which are formed by flat radial vanes. The fluid enters the impeller pockets through a suction port, formed in the stationary part of pump, where its velocity is increased and hence it is directed to the collecting passage, where it is collected and then leaves the pump through delivery port in collecting passage.

D

rpm

Collecting passage

impeller

Figure (4.1) An effort is made to make a simple theoretical model to examine the performance of such pump when water is used as working medium. Effect of operating conditions and pump dimensions is studied using

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CHAPTER 4


the present proposed model; the friction and other losses are not considered in the present analysis.

4.2 Governing Equations y n V

B dS

x

z

S

Figure (4.2) Fixed control volume

4.2.1Principle: Mass can be neither created nor destroyed. Continuity equation: ∂ ∂t

∫∫∫ ρdv + ∫∫ ρV ⋅ dS = 0 v

s

4.2.2 Principle: Time rate of change of momentum of a body equals the net force exerted on it. Momentum equation: ∂ ρVdv+ ∫∫(ρV ⋅ dS)V = ∫∫∫ρfdv− ∫∫ PdS ∂t ∫∫∫ v s v s

where v: the volume of the control volume, s: the area of closed surface (58)

CHAPTER 4


n: unit vector normal to surface at B, dS: the elemental surface area around B, define dS=n ds. ρ: the density at B and V: the velocity at B. The flow inside the pump is described by the integral form of continuity and momentum equations. Referring to Figure (4.1) the fluid enters the collecting passage with neglecting velocity. The velocity of out let is the tangential velocity. Figure (4.3) shows a part of collecting passage, which is considered as a differential control volume of length δl. Applying the conservation laws on this element Where equations (1) and (2) are continuity and momentum equations respectively. As it is clear, these equations satisfy the steady state condition.

δl

P+δP c+ δc Q+δ Q

P C Q Po Co Qo δl Figure (4.2)

Q: is the volume flow rate at the inlet cross-section of time control volume. Qo: is the volume flow rate per unit length of the collecting passage,

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CHAPTER 4


which enters the control volume coming from the pump impeller. A: is the cross-sectional area of the collecting passage. P: is the pressure at inlet of the control volume. c: is the fluid velocity at inlet of the control volume. co: is the fluid velocity coming from the impeller. Q+δ Q = Q+Qo δ l……(4.1) (p+dp)*A - (p*A) = Co δ Qo δ l-Cδ Q…….(4.2)

4.3 The Numerical Procedure In the following sections, the numerical technique and the carried out steps to predict the pump performance at different conditions are presented. For simplicity assume that, the tangential velocity acquired due to the flowing of fluid in the impeller is calculated based on the mean diameter of the impeller as shown in figure (4.1). This velocity is calculated according to following relation as : πN co = D ………(4.3) 60 N: is the speed of impeller in rpm. The change of the other two components of the velocities is neglected. The effect of mechanical friction and the viscous force is also neglected. The maximum possible flow rate per unit length of collecting passage Q0,max is given according to the relation;

Qo , max =

Vs N ………(4.4) 60πD

Where Vs the volume of impeller pockets. The volume of the pockets is given according to the following relation as;

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CHAPTER 4


Vs=(1/2)(π2r2D)-(1/2)( πr2kt) Vs=(1/2)(π2r2D)(1-kt/πD)………(4.5) Where Volume of ring as shown in figure (4.1) equal to (1/2)(π2r2D) and total volume of blades equal to (1/2)( πr2kt) K: is the total number of pockets t: is the mean thickness of the blade. r: is the radius of the pocket cross section, D: is mean diameter of the ring, δl P+δP C P Q

c

δl πD Co Qo

b) Cells identification of both collecting passage (above) and impeller

a) Mass and energy transfer through general cell of collecting passage

Figure(4.3) Governing equations are integrated by dividing the collecting passage to infinite cells (δl go to zero), as shown in figure (4.3). Referring to figure (3-a), the application of conservation laws on the shown general cell yields to the following relations as: From continuity equation Qo δl=Q………(4.6)

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CHAPTER 4


From momentum equation PA-(P+δP)A=Cρ Q-Coρ Qoδl δP=P+Qoδlρ(Co-C)/A………(4.7) from equations (4.6) and(4.7) δP=Qoρ(Co-Q/A)/A δl ..........(4.8) by integrated equation(4.8) P2

l

∫dP= ∫Q ρ(C -Q/A)/A…….(4.9) o

Where

P1

o

0

l=π D P1nad P2 are suction and delivery pressures. P2-P1=Qoρ l(Co-Q/A)/A……..(4.10) Put

∆P=P2-P1 ∆P= Qoρ l(Co-Q/A)/A

But ∆Η= ∆P/ρ g Then

∆Η=

Qo l Q (Co − ) ………(4.11) Ag A

Where ∆Η is the imparting head to the working fluid by the impeller. Water horse power WHP=ρ∆H Q/75………(4.12) If the working fluid is water and Q in [lit/s] WHP=const ∆H Q Substituting by the value of ∆H in equation (4.11) (62)

CHAPTER 4


2 Q l Q o WHP= const (CoQ − ) ………(4.13) Ag A

To get maximum WHP differentiate equation (4.13) with respect to Q

Q l 2Q ∂ WHP = const o ( C o − )=0 A ∂Q Ag From above equation maximum WHP at

Q=CoA/2.

To calculate the pressure gain at different possible flow rates, a computer program is designed to simulate the previously described theoretical model. This program is designed such that, one can study the effect of various operating conditions and the characteristic dimensions of the pump. From equation (4.11) for fixed all variable except the length of the impeller channel it is easy to study the way of which the pressure increase along the impeller channel l l=πD or

l=θ π D/360

where θ: the angle measured from inlet port towards outlet port (i.e.θ=0.0 at inlet port and θ=360 at outlet port) then ∆H=constant * θ........(4.12)

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CHAPTER 5

DESIGN AND CONSTRUCTURE OF TESTED PUMP

CHAPTER 5

DESIGN AND CONSTRUCTION OF TESTED PUMP 5.1 Engineering Design Problem Complete solution of any mechanical design problem requires the following three method: a) Empirical method, b) Rational method, and c) Experimental method. The empirical design method is based upon intuition and good engineering judgement on the part of the designer. The designer usually makes his judgment that is an outcome of his or other designer past experience of working on similar design. The information and data available in the form of “thump rules” in handbooks and codes also helps the designer using empirical methods. Since this method of design is mainly based upon the judgment of the designer, which may prove to be wrong, it can not be relied upon especially in the case of design of complex systems. The rational design method is strictly based upon well established scientific laws and relationships. These laws and relationships are mainly available in the areas of mechanics and thermodynamics, rather scarce. Therefore, in areas other than

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CHAPTER 5


mechanics and thermodynamics, the use of rational design method have a very limited scope. It is clear from above that no doubt empirical and rational design method are available for design of equipment and systems used in mechanical engineering, none of these two methods in practice individually or collectively is capable of solving satisfactorily even elementary design problems and required the experimental design method. This method is based upon correlated measurements of all the physical quantities involved. The experimental design method has paved the way for research and development. Development means experimental design. In the design method, the product based upon an initial design is tested. Accurate and correlated measurements of all physics quantities involved are done. The results are scientifically analyzed and errors are wisely interpreted. Then by trial and error method, the parameters are adjusted till the product or system designed gives the desired performance. It should be understood that the trial and error procedure is not a random one. The trials are intelligently made. In fact, experimental design requires the greatest application of engineering ingenuity. 5.2 General Procedure in Machine Design In designing a machine component, there no rigid rule. The problem may be attempted in several ways. However, the general procedure to solve a design problem is as follows:

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CHAPTER 5

1.


First of all make a complete statement of the problem, indicating the purpose for which the machine is to be designed.

2.

Select the possible groups of mechanisms, which will give the desired motion.

3.

Find the force acting on each member of the machine and the energy transmitted by each member.

4.

Select the material best suited for each member of the machine.

5.

Find the size of each member of the machine by considering the forces acting and the permissible stresses for the material used. It should be kept in mined that each member dose not deflect or deform than the permissible limit.

6.

Modify the size of the member to agree with the past experiences and judgment facilities manufacture.

7.

Draw the detailed drawing of each component and the assembly of the machine with complete specification for the manufacturing processes suggested.

5.3 The Purpose of The Pump The regenerative turbine pumps have not been as broadly used as other types of impeller pumps; a specific test has not been established for the regenerative turbine pump. So it is required to test the performance of this type of pump.

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CHAPTER 5


5.4 Structure of Tested Pump 5.4.1 Case: The case is the outer cover of the pump and it contains and supports other components. 5.4.2 Impeller It is the rotating disc, which imparts the energy to the working fluid. 5.4.3 Shaft The shaft is used to transmit the power from electric motor to the impeller. 5.4.4 Bearings Are used to support the shaft in case and reduce the friction between them. 5.4.5 Oil seals Are used to prevent the leakage of working fluid. 5.5 Forces Acting on The Parts of The Pump Based on arbitrary selection of the pump dimension we can predict the maximum delivery pressure and consumed power from theoretical model. These chosen dimensions are listed in the following table: Mean diameter Collecting passage diameter Blade thickness Number of blades

D=15.25 cm D=3.5 cm t=10.3 mm k=16

Maximum rotating speed N=3000 rpm

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CHAPTER 5


The physical properties and parameter depending on the speed of the impeller and pump dimensions are listed in the following table: Volume of pockets V Maximum flow rate per unit length of collecting passage Qo,max Tangential velocity of the impeller Co Maximum delivery head Hmax Maximum horsepower WHP Break horsepower BHP

1.512*10-4 m3 0.016 [m3/s]/m 24 m/s 20 m water 1.8 hp 15 hp

5.5.1 Radial Force Acting on The Shaft Fr The impeller of an operating regenerative turbine pump is subjected to axial and radial thrust transmitted to the shaft. The axial thrust is caused by the difference between pressures applied to the impeller end faces in axial clearance. The axial force is small, easily taken by radial thrust ball bearing. The radial thrust is due to a non uniform pressure distribution in the discharge passage, the pressure varies, as suggested by equation

H=constant*θ

Psin dθ

Figure (5.1) (68)

Pcos θ

CHAPTER 5


H=

Qo Q θ (C o − )π D Ag A 360

The elementary radial thrust acting over the length Ddθ/2 of discharge passage and width b of the impeller will be:

⎡ D ρ gH ⎤ dF r = ⎢ b ⋅ θ ⎥ sin θ d θ 2 2 π ⎣ ⎦

ρ gHbD 2 π Fr = θ sin θ d θ ∫ 4π 0 ρ gHbD [− θ cos θ + sin θ = 4π − ρ gHbd =

2

b=0.021 m then

Fr=360 N

5.5.2 Torque on The Shaft T

T =

BHP

where

ω : Angular velocity

ω = then

ω π DN 60

T=34.5 N.m

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* 735

]02 π

CHAPTER 5


5.6 Material selection 5.6.1 Classification of Engineering Material The engineering material are mainly classified as: 1. Metals and their alloys, such as iron, steel, copper, aluminum etc.

2. Non-metals, such as glass, rubber, plastic etc. The metals may be further classified as: (a)

Ferrous metals, and

(b)

Non-ferrous metals.

The ferrous metals are those, which have the iron as their main constituent, such as cast iron, wrought iron and steel. The non-ferrous metals are those, which have a metal other than iron as their main constituent, such as copper, aluminum, brass, tin, zinc etc. 5.6.2 Choice of Material for Engineering Purposes The choice of materials, for engineering purposes, depends upon the following factors: 1. Availability of the materials, 2. Suitability of the materials for the working condition in service, and 3. The cost of the materials The important properties, which determine the utility of the material, are physical, chemical and mechanical properties.

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CHAPTER 5


From the pervious information the suitable selection of the material in the following table: Element

Material

1. Case 2. Impeller 3. Shaft

Cast iron Aluminum Commercial steel

5.6.3 Properties of Selected Materials 5.6.3.1 Cast Iron The cast iron is obtained by re-melting pig iron with coke and limestone in a furnace known as cupola. It is primarily an alloy of iron and carbon. The carbon content in cast iron varies from 1.7% to 4.5%. It also contain small amount of silicon, manganese, phosphorus and sulphur. The carbon in the cast iron is present in either of the following two forms: 1. Free carbon or graphite, and 2. Combined carbon or cementite. Since the cast iron is a brittle material, therefore, it can not be used in those parts of machine which are subjected to shocks. The properties of cast iron which make it a valuable material for engineering

purposes

are

its

low

cost,

good

casting

characteristics, high compressive strength, wear resistance and excellent machinability. The compressive strength of cast iron is much greater than the tensile strength. The following are the values of ultimate strength of cast iron

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CHAPTER 5


Tensile strength Compressive strength Shear strength

100 to 200 MPa 400 to 1000 MPa 120 MPa

5.6.3.2 Commercial Steel (Carbon Steel) A carbon steel is defined as a steel which, has its properties mainly due to its carbon content and dose not contain more than 0.5% of silicon and 1.5% of manganese. The following are the values of yield strength of steel Tensile strength Compressive strength Shear strength

260 500 145

MPa Mpa Mpa

5.6.3.3 Aluminum Alloys The aluminum may be alloyed with one or more other elements like copper, magnesium, manganese, silicon and nickel. The addition of small quantities of alloying elements converts the soft and weak metal into hard and strong metal, while still retaining its light weight. The following are the values of yield strength of aluminum Tensile strength Shear strength

95 55

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MPa Mpa

CHAPTER 5


5.7 Design of The Pump 5.7.1 Design of Shaft ΣForces in radial direction =0

10 cm

2 cm

T

Fr+R2-R1=0 R1=430 N

Fr R1

R2=72 N

T

Twisting moment T=34.5 N.m Bending moment M

R2

Fr

M=Fr*0.02+R2*0.1 then

M=14.4 N.m

Equivalent twisting moment

Te = then

Te

(M 2 + T 2 )

Te=37.52 N.m

Equivalent bending moment

Me

M e = 0.5 * ( M + ( M 2 + T 2 ) then

Me=26 N.m

but

Te=π Fs ds3/32

and

Me= π Fb ds3/32

where Fs: Shear stress induced due to twisting moment. Fb: Bending stress induced due to bending moment. ds: Shaft diameter. For commercial steel Fs=800 kg.cm

and

Fb=1150 kg.cm

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(yield value)

CHAPTER 5


Based on twisting stress ds=1.32 cm Based on bending stress ds=1.7 cm Take factor of safety

fs=1.5

Then the minimum shaft diameter ds=2.5 cm 5.7.2 Design of Impeller 5.7.2.1 Blade Thickness t Maximum pressure acting on the blade P=196.2 kPa The force acting on the blade F=P*A where A is the cross sectional area of the

A

blade as shown in figure.

Fs =

t

P⋅A = 1 π dt 2 Pd = 4t =

where

F a P

1 π 2 ⋅ d 2 4 1 π dt 2

d: the collecting passage diameter, and a: the contact area of the blade with the impeller. then t=0.22 mm

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CHAPTER 5


5.7.2.2 Minimum Thickness of The Impeller

1 π dl 2 Ft = t \l Pπd = t\ P⋅

t\

Pπd

then t \ = 2 Ft where

t\ : the minimum thickness of the impeller Ft: Tensile stress. then

t\=0.04 mm

5.7.3 Design of Casing The minimum thickness of the case tc

tc = Then

Pd 2 Ft

tc=0.1 mm

Note: The minimum thickness can be casting is 6mm. 5.8 Manufacture of Tested Pump The manufacture of tested pump is passes through three processes casting and machined. Which are discussed in the following paragraphs. 5.8.1 Casting Process Practically all the detailed operation that enter into the making of sand casting may be categorized as belonging to one of five fundamental steps of the process:

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CHAPTER 5


1. Patternmaking 2. Coremaking 3. Molding 4. Melting and pouring 5. Cleaning 5.8.1.1 Patternmaking Patterns are required to make molds. The mold is made by packing some readily formed plastic material, such as molding sand, around the pattern. When the pattern is drawn, its imprint provide the mold cavity which is ultimately filled with metal to become the casting. Thus molding requires, first, that material be made. A pattern may be simply visualized as approximate replica of the exterior of a casting. If the casting is to be hollow, as in the case of pipe fitting, additional pattern, referred to as core box, are used to form the sand that is used to create these cavities. See (fig (5.1))

Figure (5.2) Patten of the pump (76)

CHAPTER 5


5.8.1.2 Coremaking Cores are forms usually made of sand, which are placed into a mold cavity to form the interior surface of casting thus the void space between the core and mold-cavity surface is what eventually becomes the casting.

5.8.1.3 Molding Molding consists of all operations necessary to prepare a mold for receiving molten metal. Molding usually in valves placing a molding aggregate around a pattern held within a supporting frame, with drawing the pattern to leave the mold cavity, setting the cores in the mold cavity, and finishing and closing the mold. The mold is then ready for pouring. 5.8.1.4 Melting and Pouring The preparation of molten metal for casting is referred to simply as melting. Melting is usually done in a specifically are of the foundry, and the molten metal is transferred to the molding area where the molds are poured. 5.8.1.5 Cleaning Cleaning refers to all operations necessary to the removal of sand, scale, and excess metal from the casing. The casing is separated from the molding sand and transported to the cleaning department. Burned-on sand and scale are removed to improve the surface appearance of the casting. Excess metal, in the form of fins, wires, parting line fins and gates is cut off. Defective

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CHAPTER 5


castings may be salvaged by wilding or other repair. The casting is then ready for machining. The preceding paragraphs have briefly summarized the basic steps in the foundry process. 5.8.2 The Lathe Work The main function of this operation is cleaning surface of case and impeller, removing the excess metal.

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CHAPTER 6

EXPERIMENTAL WORK

Chapter 6

EXPRIMENTAL WORK 6.1 Test pump There are many pump designs available. Each having its own specific set of operating parameters. In the fluid power industry the more common types of pumps include gear, vane and piston. In open loop and closed loop systems. In the vane and piston category we have fixed-displacement as well as variable-displacement pump types.

All pump tests are similar with particular attention paid to fluid type, viscosity, outlet pressure, flow, drive speed and inlet conditions. There are a few pump designs that are exceptions. Examples are metering pumps. Which provide pulse output, centrifugal pumps under design or test “Regenerative turbine pump” which have a highly dependent pressure versus flow curve relation ship.

Pump testing can be fairly simple or may involve the use of complex equipment. (See fig.(6.1)) to measure all parameters required. Depending on who performs the test, the test methods used, the location and accuracy of the instrumentation used. Pump test data may be highly accurate or in error by as much as 25%. This is particularly true when flow meters misapplied in a

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CHAPTER 6

EXPERIMENTAL WORK

Figure (6.1) Figure shows the test stand of the pump

Figure (6.2) shows the pump parts and its construction (80)

CHAPTER 6

EXPERIMENTAL WORK

test circuit like the circuit used. In all cases, the pump test circuit and instrumentation must all be engineered into a single package to ensure accurate results.

This section discusses the more common tests applied to the regenerative turbine pump.

6.1 Description of Hydraulic Circuit ¾ Tested pump ¾ Flexible coupling ¾ Electric motor ¾ Two water tank ¾ Test Rig

Instrumentation ¾ Control panel ¾ Torquemeter 6.1.1 Tested Pump Regenerative turbine pump that is under design and test. (See fig. (6.2)) consists of casing, impeller, shaft, bearing, oil seal and fixing bolts. (For more details see chapter 5) 6.1.2 Flexible Coupling We have already discussed that a flexible coupling is used to join the abutting ends of shafts when they are not in exact (81)

CHAPTER 6

EXPERIMENTAL WORK

alignment in the case of a direct-coupled drive from a prime mover to an electric generator. We should have four bearing at comparatively close distance. In such a case and many others, as in a direct electric drive from an electric motor to a machine tool, a flexible coupling is used so as to permit an axial misalignment of the shafts without undue absorption of power that the shafts are transmitting. In the following are the different types of flexible coupling: 1-oldham’s coupling, 2-universal coupling, and 3-bushed pin flexible coupling (our coupling) (See fig. (6.3))

6.1.3 Electric Motor An electric motor has the following data: Horsepower 20 HP

2920 rpm

Current 29.2 A

Volt 380 V

Frequency 50 HZ

3 phase

Ambient temp. 40 oC

Variable speed

(See fig. (6.4)) 6.1.4 Test Rig In the test under consideration two water tank are used, one for suction with the maximum volume scale 125 liter, and the second for delivery with scale of maximum volume 50 liter. (See fig. (1)) (82)

CHAPTER 6

EXPERIMENTAL WORK

Figure (6.3) Torquemeter

Figure (6.4) Variable Speed Electric Motor

Figure (6.5) Control Panel (83)

CHAPTER 6

EXPERIMENTAL WORK

6.1.5 Control Panel It is a device used to convert the electrical signals coming from the torque meter to a calibrated numbers on the lighted digital display rounded to first decimal. And it contain pressure gage, which used to measure the delivery pressure in bars. An on/off switch does control of electric motor, and the speed switch, which is, vary the electric frequency hence the motor speed is varied. (See fig (6.5))

6.1.6 Torquemeter It is a device that measures the torque and speed. By methods of brushes. The device senses with torque and speed then transforms it to electrical signals with mille volts by means of transducers then the control panel calculates the horsepower by the formula:

torque(lb.in) 2πN * 60 12 power (hp) = 550

power ( hp ) =

torque ( lb .in ) * rpm 63025 . 36

where Torque is measured in pound per inch (lb.in) N: rpm (See fig. (6.3))

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CHAPTER 6

EXPERIMENTAL WORK

6.2 Description of The Test There are four quantities must be measured at every reading in the first the motor speed, which is kept constant at that test and obtained from the digital display. The second is the pressure, which is controlled by a valve, the reading of the pressure gage indicates the pressure in bar. Head in [m water] = pressure [bar] *10.193 The third is the volume and time corresponding to that pressure the volume is obtained from the reading of the calibrated tank and the time is measure by a digital stopwatch. In the last the break horsepower (BHP) or the torque, BHP and torque are indicated for each other.

6.2.1 The Procedure of The Test This procedure is consist of nine steps as follow: 1. Fill in the intake tank (suction tank) with water in order to be higher than the pump to fill it with water. 2. Open

the

valve

at

(for

example

fully

opened

corresponding the maximum flow rate and minimum system resistance). 3. Start the electric motor. 4. Control the motor speed to reach a specific speed. 5. Measure the volume in the delivery tank (calibrated) and the corresponding time.

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CHAPTER 6

EXPERIMENTAL WORK

6. From control panel read the break horsepower and the torque. 7. Score the data pressure, volume, time, BHP and torque in a table. 8. Change the valve opening and score data that in step (7). 9. Repeat the above steps from 1 to 8 for anther speed starting from 400 rpm with step 200 rpm (for about 6 speeds).

6.3 Empirical Formula We can correlate the reading of the test at different speed to obtain a relation ship to describe the performance of the regenerative turbine pump. This relation can be predicted from the theoretical formula.

∆H =

QoπD ⎡ Q⎤ C − o Ag ⎢⎣ A ⎥⎦

(πD − kt) N 2 (πD − kt) N ∆H = k1 ⋅ − k2 ⋅Q 2 D g gDd Where k1 a4nd k2 ∆H=c1β0a −c2β1b Q where

⎡ (π D − kt ) DN 2 ⎤ βo = ⎢ ⎥ g ⎣ ⎦ ⎡ (π D − kt ) N ⎤ β1 = ⎢ ⎥ gd 2 ⎣ ⎦ (86)

CHAPTER 6

EXPERIMENTAL WORK

ho=coβoa Where ho is the head at shut off condition (Q=0) To convert the above equation in a linear form ln(ho)=ln(co)+a ln(βo) put

y= ln(ho) ,c= ln(co) and x= ln(βo)

using least square method Σy=n c+a Σx Σxy= c Σx+a Σx2 where n is the number of reading by solving the above two simultaneous equation the values of c and a are obtained. c=-7.55499 and a=1.05055 then ⎡ (πD − kt ) DΝ 2 ⎤ h o = 3.77155×103 * ⎢ ⎥ g ⎣ ⎦

1.05067

we can write the equation as: h=ho-c1β1bQ (ho-h)/Q=c1β1b To convert the above equation in a linear form ln((ho-h)/Q)=ln(c1)+b ln(β1) put

z= ln((ho-h)/Q),c= ln(c1) and x= ln(β1)

using least square method

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CHAPTER 6

EXPERIMENTAL WORK

Σz=n c+b Σx Σxz= c Σx+b Σx2 Where n is the number of reading By solving the above two simultaneous equation the values of c and a are obtained. c=9.99136 and b=-0.00431446 Then the empirical formula is ⎡ (πD − kt )DΝ2 ⎤ h = 3.77155×103 * ⎢ ⎥ g ⎣ ⎦

1.05067

where Q in [lit/min], All dimensions in [m] and N [rpm]

(88)

⎡ (πD − kt) N ⎤ − 0.36395⎢ ⎥ 2 ⎣ gd ⎦

−0.00431446

⋅Q

Chapter 7

RESULTS AND DISCUSSION

Chapter 7

RESULTS AND DISCUSSION 7.1 Introduction In this chapter the results from theoretical modeling of the regenerative turbine pump and the actual performance of that pump will be discussed. In theoretical modeling the various parameters are checked e.g. (mean diameter, number of blades, speed, etc) In actual performance two impellers of different number of blades (10 and 20 blades) can be compared with each other, and two impeller of different clearance (0.25 mm and 1.5 mm) between the impeller and the case of collecting passage side.

7.2 Results of Theoretical model In the following, the effect of impeller speed is presented. Also effect of pump size on its performance is shown. In these figures, a pump of (0.2 m) mean impeller diameter D and of (0.03 m) pocket radius r is studied [(see figure (1))] Impeller speed, in this case is taken as (1500 rpm) and suction pressure is (1 atm).

89

Chapter 7


∆H ∆Hmax

360

Figure (7.1)

θ

Figure (7.1) shows the pressure distribution along the collecting passage at constant values of

flow rate. As it is clear, the

pressure increases gradually in the down stream direction till it reaches its maximum value at the exit of the passage (corresponding to θ=360o).

7.2.1 Effect of impeller speed Figures (7.2) and (7.3), the effect of impeller speed on the pump performance is presented. Impeller of (0.20 m) mean diameter and (0.6 m) pocket diameter is examined in this figures delivery pressure versus flow rate and water horsepower versus flow rate are depicted.

90

Chapter 7


7.2.1.1 Effect of speed of impeller on the delivery pressure As it is shown, the delivery pressure is increased as the impeller speed increases. For every speed the pressure decreases as the flow rate increases, the maximum value of delivery pressure at Q is equal to 0.0(shut off). As it is well known, the maximum represents the undesirable operation point of the pump for along time. 120

100

N=3100rpm

H m water

80

2800

60 2500

40

2200 1900

20 1300

1600

1000

700

0 0

10

20

30

40

50

60

70

Q, lit/s

Figure (7.2) Effect of speed of impeller on the delivery pressure

91

80

90

Chapter 7


7.2.1.2 Effect of speed of impeller on the horsepower As it is shown, water horsepower is increased as the impeller speed increases. For every speed the water horsepower increases as the flow rate increases till it reaches a maximum value at Q=CoA/2. After this maximal value, the WHP decreases sharply for higher speeds. 0.035

0.03

N = 3100 rpm

0.025 2800

HP

0.02

2500

0.015

2200

0.01 1900 0.005 1600 1300

1000

0 0

10

20

30

40

50

60

70

Q, lit/s

Figure (7.3) Effect of speed of impeller on the horsepower

92

80

90

Chapter 7


7.2.2 Effect of the mean diameter of the impeller Figures (7.4) and (7.5) shows the effect of mean diameter of the impeller on the performance of pump the same previously mentioned impeller is examined.

7.2.2.1 Effect of the mean diameter of the impeller on the delivery pressure As it is shown, the delivery pressure is increased as the impeller mean diameter increases. For every speed the pressure decreases as the flow rate increases. 35

30

D=0.225m 25

20

HP

D=0.2m

15 D=0.175 10 D=0.15m 0.1 5 0.075

0.125

0 0

10

20

30

40

50

Q, lit/s

Figure (7.4) Effect of the mean diameter of the impeller on the delivery pressure

93

60

Chapter 7


7.2.2.2 Effect of the mean diameter of the impeller on the WHP As it is shown in figure (7.5), water horsepower is increased as the impeller mean diameter increases. For every mean diameter the water horsepower increases as the flow rate increases till it reaches a maximum value at Q=CoA/2. After this maximal value, the water horsepower decreases. 0.007

0.006 D=0.225 m

0.005

HP

0.004 D=0.2m

0.003

0.002 D=0.175

0.001

D=0.15m 0.125 0.1

0 0

10

20

30

40

50

Q, lit/s

Figure (7.5) Effect of the mean diameter of the impeller on the WHP

94

60

Chapter 7


7.2.3 Effect of the ratio of channel diameter to the mean diameter of the impeller Figures (7.6) and (7.7) shows the effect of the ratio of channel diameter to the mean diameter of the impeller on the performance of pump the same previously mentioned impeller is examined.

7.2.3.1 Effect of the ratio of channel diameter to the mean diameter of the impeller on the delivery pressure As shown in the figure (7.6) the maximum pressure is maintain constant with different values of the ratio of channel diameter to mean diameter of the impeller [rd], but the maximum flow rate increase with the increase of rd. 30

25

H m water

20

15 rd=0.15

rd=0.1

rd=0.2

rd=0.25

10

5

0 0

10

20

30

40

50

60

70

Q, lit/s

Figure (7.6) Effect of the ratio of channel diameter to the mean diameter of the impeller on delivery pressure

95

Chapter 7


7.2.3.2 Effect of the ratio of channel diameter to the mean diameter of the impeller on horsepower As it is shown in figure (7.7), water horsepower is increased as the ratio of channel diameter to the impeller mean diameter increases. For every ratio of channel diameter to the impeller mean diameter the water horsepower increases as the flow rate increases till it reaches a maximum value. After this maximal value, the water horsepower decreases

0.006 rd=0.25 0.005

0.004

HP

rd=0.2 0.003

0.002 rd=0.15

0.001

rd=0.1

0 0

10

20

30

40

50

60

Q, lit/s

Figure (7.7) Effect of the ratio of channel diameter to the mean diameter of the impeller on horsepower

96

70

Chapter 7


7.2.4 Effect of the number of blade Figures (7.8) and (7.9) shows the effect of the number of blades on the performance of pump the same previously mentioned impeller is examined. The delivery pressure and water horse power are decrease as the number of blades increase. 9 8 7

H m water

6 k=10 5 4 3

k=15

2

k=17

1 0 0

2

4

6

8

10

12

Q, lit/s

Figure (7.8) Effect of number of blades on the delivery pressure 0.25 K=10 0.2

HP

0.15 K=15 0.1 K=17 0.05

0 0

1

2

3

4

5

6

7

Q, lit/s

Figure (7.9) Effect of number of blades on the horsepower

97

8

9

Chapter 7


7.3 Results of Experimental work In experimental work many parameter affecting on the performance of the regenerative pump are tested e.g. (speed, number of blades, and clearance). Three impellers are used each one has a specific dimension and number of blades. The specific dimension and number of blades of the first impeller are shown in the following table Mean diameter

152.5 mm

Collecting passage diameter

28 mm

Mean thickness of blades

10.3 mm

Number of blades

10

This impeller will be denoted by Impeller k10. The specific dimension and number of blades of the first impeller are shown in the following table Mean diameter

152.5 mm


32 mm


10.0 mm

Number of blades

16

This impeller will be denoted by Impeller k16. The specific dimension and number of blades of the first impeller are shown in the following table Mean diameter

152.5 mm


32 mm


10.3 mm

Number of blades

20

98

Chapter 7


This impeller will be denoted by Impeller k20 where k means the number of blades. 7.3.1 Performance Carves of the regenerative turbine Pump 8

50

0.8

H, m water

BHP

0.6 8

4

0.4 4

12

2

8

20

Head

10

1

4

0

0

BHP

BHP Efficiency

Efficiency

0

0.0 20 40 Flow rate, lit/ min

0

0

60

0

Figure (7.10) Performance curves of impeller k10 at speed 1200 rpm

20

40 Q, lit/ min

16

10

1

8 12 1

BHP

6 8

4 0 4 2

Head BHP Efficiency

0

0

0 0

60

Figure (7.11) Performance curves of impeller k16 at speed 1200 rpm

20

40

60

Q, lit/ min

Figure (7.12) Performance curves of impeller k20 at speed 1200 rpm 99

Efficiency

0

3

30

2 0.2

Head

16

40

6

H, m water

H ead, m water

12

4

Efficiency, %

1.0

BHP

16

Chapter 7


7.3.2 The Effect of Speed on the Performance In figures (7.13, 7.14, ….7.21) the effect of speed of impeller is shown on various impeller of different number of blades and different clearance. 7.3.2.1 Effect of speed on the delivery Pressure 60 30

Head at speeds

Head at Speed

600 rpm

400 rpm

800 rpm

600 rpm

1000 rpm

800 rpm

1200 rpm

1000 rpm

1400 rpm

40

1800 rpm

20

1400 rpm

20 10

0

0 0

20

40

60

80

100

Q, lit/ min

0

20

40

60

80

Q, lit/ min

Figure (7.13) Effect of speed on the delivery pressure of impeller k10


As it is shown from above

16

Head at speed 400 rpm

figures, the delivery pressure is

600 rpm 800 rpm

increased as the impeller speed increases. For every speed the pressure decreases as the flow

12

1000 rpm 1200 rpm

H, m water

H, m water

1200 rpm

H, m water

1600 rpm

rate increases, the maximum

1400 rpm

8

4

value of delivery pressure at Q is equal to 0.0 (shut off). As it is

0

well known, the maximum represents the undesirable operation point of the 100

0

20

40

60

Q, lit/min


80

Chapter 7


pump for along time. 7.3.2.2 Effect of Speed on Break horse Power (BHP) 5

4

Speed 600 rpm 800 rpm

4

1000 rpm

3

1200 rpm 1400 rpm 1600 rpm

3

BHP

BHP

1800 rpm

2 Speed

2

400 rpm 600 rpm

1

800 rpm

1

1000 rpm 1200 rpm 1400 rpm

0

0 0

20

40 60 Q, lit/ min

80

0

100

Figure (7.16) Effect of speed on BHP of impeller k10

20

40 60 Q, lit/ min

80

100

Figure (7.17) Effect of speed on BHP of impeller k16 1.6

As it is shown from above 1.2

figures, the BHP is increased as the impeller speed BHP decreases as the flow

0.8

BHP

increases. For every speed the rate increases, the maximum

Speeds 400 rpm 600 rpm

0.4

800 rpm 1000 rpm

value of BHP at Q is equal

1200 rpm 1400 rpm

0.0

to 0.0 (shut off).

0

20

40

60

80

Q, lit/ min

Figure (7.18) Effect of speed on BHP of impeller k20

101

Chapter 7


7.3.2.3 Effect of Speed on Mechanical losses This test is done by impeller k16 at different speeds from (600 rpm to 2000 rpm) 1.20

Mechanical loss [HP]

1.00

0.80

0.60

0.40

0.20

0.00 400.00

800.00

1200.00 Speed [rpm]

1600.00

2000.00

Figure (7.19) From figure (7.28) it is clear that the horse power required to over come the mechanical loss increase as the speed increase.

102

Chapter 7


7.3.2.4 Effect of Speed on Overall Efficiency

8

16

6

Speed

4

600 rpm

Efficiency %

20

12

Speed

8

400 rpm 600 rpm

800 rpm 1000 rpm

2

800 rpm

4

1200 rpm

1000 rpm

1400 rpm

1200 rpm

1600 rpm

1400 rpm

1800 rpm

0 0

20

40 60 Q, lit/ min

80

0 0

100

Figure (7.20) Effect of speed on the overall efficiency of impeller k10

20

40 Q, lit/ min

60

80

Figure (7.21) Effect of speed on the overall efficiency of impeller k16 10

As it is shown from above N=1400 rpm

figures, the overall efficiency is decreased as the impeller speed increases. For every speed the overall efficiency increases as the flow rate increases maximum

8 1000

Efficincy %

Efficiecy [%]

10

6

600

1200 400

800 Speed

4 600 rpm 800 rpm 1000 rpm

2

1200 rpm

till it reach the efficiency then

decrease as flow rate increase.

103

1400 rpm 1600 rpm

0 0

20

40 Q, lit/ min

60

80

Figure (7.22) Effect of speed on the overall efficiency of impeller k20

Chapter 7


7.3.3 Effect of Number of blades on the performance Figures (7.23, 7.24, 7.25) show the effect of number of blades on the performance of regenerative turbine pump. Two impellers (k10 and k20) are tested, at the same speed (1200 rpm). 7.3.3.1 Effect of Number of blades on the delivery Pressure Figure (7.23) shows the effect of number of blades on the delivery pressure. 16

Number of blades 10 blades 20 blades

H, m water

12

8

4

0 0

10

20 30 Q, lit/ min

40

50

Figure (7.23) Effect of number of blades on the delivery pressure

As shown the increase of number of blades increase the delivery pressure and flow rate. As discussed in chapter 3 (when the flow is more guided the helical spring of the flow is compressed thus the working fluid is filled impeller pocket many times then imparted more energy)

104

Chapter 7


7.3.3.2 The Effect of Number of Blades on the BHP Figure (7.24) shows the effect of number of blades on the BHP. 1.00

0.80

BHP

0.60

0.40

Number of blades

0.20

20 blades 10 blades

0.00 0

10

20 30 Q, lit/ min

40

50

Figure (7.24) shows the effect of number of blades on the BHP.

As shown in the figure (7.19) the BHP increases with the number of blades as the delivery pressure and corresponding flow rate increases.

105

Chapter 7


7.3.3.3 The Effect of number of blades on the overall Efficiency. Figure (7.25) shows the effect of number of blades on the overall efficiency. 10

Efficiency [%]

8

6

4

Number of blades 2

10 Blades 20 Blades 0 0

10

20 30 Q, lit/ min

40

50

Figure (7.25) Effect of number of blades on the overall efficiency.

As shown in the figure (7.25) the overall efficiency increases with the number of blades.

106

Chapter 7


7.3.4 Effect of Clearance Between Blades and Case on the performance Figures (7.26, 7.27, 7.28) show the effect of clearance between blades and case on the performance of regenerative turbine pump. Two impellers (k10 and k20) are tested, at the same speed (1200 rpm). 7.3.4.1 Effect of Clearance Between Blades and Case on the delivery Pressure Figure (7.26) shows the effect of number of blades on the delivery pressure. 50

Clearance 1.5 mm

40

H, m water

0.25 mm

30

20

10

0 0

20

Q, lit/ min

40

60

Figure (7.26) shows the effect of clearance on the delivery pressure.

As shown from figure (7.26) the delivery pressure decrease as the clearance increase.

107

Chapter 7


7.3.4.2 Effect of Clearance Between Blades and Case on the BHP Figure (7.27) shows the effect of number of blades on the delivery pressure. 4 Clearnce 1.5 mm 0.25 mm

BHP

3

2

1

0 0

20

40

60

Q, lit/ min Figure (7.27) shows the effect of clearance on the BHP.

As shown from figure (7.27) the BHP increases as the clearance decrease.

108

Chapter 7


7.3.4.3 Effect of Clearance Between Blades and Case on the Overall Efficiency Figure (7.28) shows the effect of number of blades on the delivery pressure. 16

Efficiency, %

12

8

4 clearnce 1.5 mm 0.25 mm

0 0

20

40

60

Q, lit/ min Figure (7.28) Effect of clearnce on the overall efficiency

As shown from figure (7.28) the overall efficiency increases as the clearance decrease. In general as a clearance increase has a bad affect on the performance.

109

Chapter 7


7.4 Correction of Theoretical Formula When

theoretical

and

actual

results

are

compared,

considerable deviation between them is appear. Thus a correction of a theoretical formula should be take place. This correction is done on the impeller k16. Theoretical formula

∆H = Corrected formula

∆H =

Q ol Q (C o − ) A Ag

Qol Q (4.68475*Co − (0.0067N + 45.719) ) A Ag

Where N is the speed of impeller [rpm] This correction is valid for

400 ≤ N ≤ 1400 7.5 Specific Speed of Regenerative turbine Pump Ns Various factors or parameter are used in practice in correlating data on performance and design. And one of the more common factors is specific speed. Which is defined as

Ns =

N Q ( gH ) 3 / 4

where N in rad/s, H and Q are measured at the point of maximum efficiency. The specific speed of tested regenerative turbine pump varies from 0.1 to 0.14.

110

CONCLUSIONS AND RECOMMENDATIONS

CONCLUSIONS AND RECOMONDATIONS

Conclusions

Regenerative turbine pumps are rarely used or tested, and many of hydraulic machines books do not provide any information about this type of pumps. So, this work is done to study theoretical analysis. Mechanical and hydraulic design, and actual performance of the pump are tested. The main contributions of this work are the following: 1.

Theoretical analysis of flow thorough the pump is constructed depending on some assumptions that simplify this analysis. And rational formula that describes the relationship between the theoretical imparted head and flow rate is obtained.

2.

Based on theoretical analysis of the pump, the mechanical design of pump parts is achieved.

3.

The theoretical analysis is compared with the actual performance of the pump and a correction of the theoretical relation and empirical formula is obtained.

4.

Some parameters that affect the performance of the pump are tested.

5.

Based on empirical and correction relations, the hydraulic design of this pump can be obtained.

111

CONCLUSIONS AND RECOMMENDATIONS

6.

Generally, these pumps have a small efficiency compared with other types, but it has great advantages that meet the requirements of industries and power stations. So it should have a sufficient chance of study.

Recommendations:

It would be interesting to study other parameters that affect the performance e.g. (mean impeller diameter, channel diameter, …etc.). Some defect in a tested pump design and manufacturing should be avoided to obtain more accurate results. The design and drawing of tested pump and a recommended design is presented in appendix “III”.

112

REFERENCES

REFERENCES 1. M.G.Wasel “Performance of Steam Regenerative Turbine Compressor,” Mansoura Engineering Journal (MEJ), Faculty of Engineering, vol.22, No.3, September 1997. 2. M.G.Wasel “Performance Analysis of Air Regenerative Turbine Compressor,”Mansoura

Engineering

Journal

(MEJ),

Faculty

of

Engineering, vol.22, No.4, September 1997. 3. M.A.Rayan “Text Book of Hydraulic machines,” 4. V.M.Cherkassy “Pumps Fans Compressors,” Mir Publisher-Mosco,1985. 5. Robert.A.Nasca “Testing fluid power components,” Industrial Press Inc, 1990. 6. R.s.Khumi,I.K,Gupta “ Text Book of Machine Design,”Urasia Poblishing Hose, 1999. 7. Ernest O.Doebelin “Measurement System Application and Design,” Mc.Graw-Hill International Book Company, 1982.

8. http://www.rothpump.com/index.html 9. http://www.grahamcorp.com/TURBINE.HTM 10. http://www.federalcorp.com/burks/graphics/turbine.htm 11. http://www.machinerysystems.com/Raving%20Fan/MTH%20Tool.html 11. http://www.munropump.com/Cindex.html 12. http://www.gspump.com/apindprc.htm 13. http://www.saladinpump.com/products.htm 14. http://www.vimpex.com/pumps.htm 15. http://www.pumping-systems.com/Pages/page3.html 16. http://www.pumpenergy.com/frmain.htm

113

APPENDIX

Appendix a ”I” The Reading Impeller Impeller speed Pressure, bar Volume,liter 0.2 20 0.3 10 0.38 0 Impeller Impeller speed Pressure, bar Volume, liter 0.2 30 0.4 20 0.5 10 0.6 0 Number of blades Impeller speed Pressure, bar Volume, liter 0.36 20 0.4 20 0.5 20 0.6 20 0.8 10 0.9 0 Impeller Impeller speed Pressure, bar Volume, liter 0.4 30 0.6 30 0.8 20 1 10 1.2 0

K10 600 rpm BHP 0.1 0.1 0

Torque, lb.in 12 14 15.5

62 77 93 …

k10 800 rpm BHP 0.3 0.3 0.3 0.3

Torque, lb.in 20.5 23 25.5 26.5

31 36 45 60 91 …

k10 1000 rpm BHP 0.5 0.5 0.5 0.5 0.6 0.6

Torque, lb.in 28.5 30 31 32.5 38 37

40 53 50 58 …

k10 1200 rpm BHP 0.6 0.7 0.8 0.8 1

Torque, lb.in 34 36 40 44 52

Time, s 54 94 0

Time, s

Time, s

Time, s

(A-1)

APPENDIX

Impeller Impeller speed Pressure, bar Volume, liter 1.65 40 2 30 2.4 30 3 30 3.6 30 4 30 4.5 30 5.3 0 Impeller Impeller speed Pressure, bar Volume, liter 0.6 30 1 30 1.4 20 1.8 10 2 0 Impeller Impeller speed Pressure, bar Volume, liter 0.8 30 1.4 30 2 20 3 0 Impeller Impeller speed Pressure, bar Volume, liter 0.2 20 0.3 10 0.4 10 0.5 0

k10 1400 rpm BHP 2.1 2.2 2.3 2.6 1.9 3.15 3.8 35

Torque, lb.in 94 100 106 115 130.5 143.5 167.5 156.5

29 35 33 32 …

k10 1600 rpm BHP 1.5 1.5 1.6 2.1 2.7

Torque, lb.in 58.5 60.5 65 83 108

20 31 33 …

k10 1800 rpm BHP 0 0 0 0

Torque, lb.in 77.5 82 100 156

58 53 86 ……

k16 400 rpm BHP 0.1 0.1 0.1 0.1

Torque, lb.in 8 8 9 10.5

Time, s 35 29 32 37 41 50 69 ……

Time, s

Time, s

Time, s

(A-2)

APPENDIX

Impeller Impeller speed Pressure, bar Volume, liter 0.36 30 0.5 30 0.7 20 0.9 10 1.05 0

k16 600 rpm Time, s BHP 60 0.1 77 0.1 94 0.2 100 0.2 …… 0.2

Torque, lb.in 13.5 15 19.5 23 25

Impeller Impeller speed Pressure, bar Volume, liter 0.6 40 0.7 40 0.9 40 1.1 30 1.3 20 1.5 20 1.7 10 1.9 0

k16 600 rpm BHP 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.7

Torque, lb.in 26 28 30.5 35 39 43 46.5 55

k16 1000 rpm BHP 0.65 0.7 0.8 1 1.1 1.4 1.5 1.8

Torque, lb.in 41.5 45 50.5 61 74 87 100 118

k16 1200 rpm BHP 1.2 1.25 1.6 1.7 1.9

Torque, lb.in 63 65.5 83 86.5 98

Number of blades Impeller speed Pressure, bar Volume, liter 0.9 40 1.1 40 1.4 40 1.8 30 2 30 2.4 20 2.7 20 3 0 Impeller Impeller speed Pressure, bar Volume, liter 1.25 30 1.4 30 1.8 30 2.1 40 2.5 30

Time, s 63 70 74 81 74 114 107 ……

Time, s 51 56 60 64 82 80 135 ……

Time, s 30 33 37 53 47 (A-3)

APPENDIX

2.8 3.1 3.5 4.1 4.3

30 30 20 5 0

Impeller Impeller speed Pressure, bar Volume, liter 1.65 40 2 30 2.4 30 3 30 3.6 30 4 30 4.5 30 5.3 0

54 66 62 129 ……

2.1 2.3 2.4 3 ----------

111.5 120.5 129 156.5 ----------

k16 1400 rpm BHP 2.1 2.2 2.3 2.6 1.9 3.15 3.8 35

Torque, lb.in 94 100 106 115 130.5 143.5 167.5 156.5

Impeller Impeller speed Pressure, bar Volume, liter Time, s 0.1 10 62 0.15 5 60 0.2 0 …

K20 400 rpm BHP 0 0 0

Torque, lb.in 6 6.5 7

Impeller Impeller speed Pressure, bar Volume, liter Time, s 0.15 10 37 0.2 10 62 0.3 0 …

K20 600 rpm BHP 0.1 0.1 0.1

Torque, lb.in 11.5 13.5 14.5

Impeller Impeller speed Pressure, bar Volume, liter 0.2 20 0.3 20 0.4 20 0.5 10 0.6 10 0.7 0

K20 800 rpm BHP 0.3 0.3 0.3 0.3 0.3 0.3

Torque, lb.in 22 23 24 24.5 26 27.5

Time, s 35 29 32 37 41 50 69 ……

Time, s 35 46 59 40 125 … (A-4)

APPENDIX

Impeller Impeller speed Pressure, bar Volume, liter 0.35 20 0.4 30 0.5 30 0.6 30 0.8 20 0.35 20 Impeller Impeller speed Pressure, bar Volume, liter 0.4 30 0.6 30 0.8 30 1 20 1.2 10 1.5 0 Impeller Impeller speed Pressure bar Volume, liter 0.6 40 0.8 30 1 30 1.2 30 1.4 20

28 49 57 76 96 28

K20 1000 rpm BHP 0.5 0.5 0.5 0.5 0.6 0.5

Torque, lb.in 30 31.5 32.5 34 35.5 30

36 44 49 49 42 …

K20 1200 rpm BHP 0.8 0.8 0.8 0.9 0.9 1

Torque, lb.in 40 42.5 43 45.5 48 52.5

42 29 39 45 40

K20 1400 rpm BHP 1.2 1.2 1.2 1.3 1.4

Torque, lb.in 53.5 54.5 56 58.5 63

Time, s

Time, s

Time, s

(A-5)

APPENDIX

Appendix “II” Computer Applications A computer program has been designed to study the effect of various parameter on the performance of regenerative turbine pump. The input file of this program must written in the following form: C this line means a comment. D this line means the mean diameter have a value between brackets in centimeters R this line means the ratio of channel diameter to mean impeller diameter have a value in a brackets K this line the number of blades have a number in the brackets. T this line means the mean thickness of the blade have a value in a brackets in centimeters. N this line means the impeller speed have a value in a brackets. V this line mean that a parameter under checking have the a first value (value1) and the last value (value2) and rich the last value in number of step (integer number). NOTE: This program dose not make any check on input file. /*******************************************************/ #include"stdio.h" #include"conio.h" #include"process.h" #include"alloc.h" #include"iostream.h" #include"math.h" double get_v(double,double,double,int); double get_Qo(double,double,double); double get_Co(double,double); double get_A(double); double get_h(double,double,double,double,double); void intermediate(double*,double,double,double,double,int,char ,double); FILE*dat,*res; //Input and output files; void main(void) { double D, //Mean diameter of the impeller. r, //Raduis of the passage.

(A-6)

APPENDIX rd,

//The ratio of raduis of the passage to //mean diameter of the impeller. N, //Impeller speed (rpm). t, //Mean thickness of the blade. from,to,step; double Q[21],Qmax,Qstep,Co,A; int i,n,val,flag=2,ln=0, k; //Number of blades. char fil[81],index,var,line[81]; do { cout>fil; dat=fopen(fil,"r"); if(!dat) { cout