CHAPTER 1 (INTRODUCTION) (INTRODUCTION) 1.1 CENTRIFUGAL PUMP Centrifugal pumps are turbomachines used for transporting liquids by raising a specified volume flow to a specified pressure level, which uses the dynamic principle of accelerating fluid, through centrifugal activity, and converting the kinetic energy into pressure.
1.2 WORKING AND ELEMENTS OF CENTRIFUGAL PUMP A centrifugal pump essentially composed of a casing, a bearing housing, the t he pump shaft and an impeller. The liquid to be pumped flows through the suction nozzle to the impeller. The overhung impeller mounted on the shaft is driven via a coupling by a motor. The impeller transfers the energy necessary to transport the fluid and accelerates it in the circumferential direction. This causes the static pressure to increase in accordance with kinetics, because the fluid flow follows a curved path. The fluid exiting the impeller is decelerated in the volute and the following diffuser in order to utilize the greatest possible part of the kinetic energy e nergy at the impeller outlet o utlet for increasing the static pressure. The diffuser forms the discharge nozzle.
Fig 1.1 Centrifugal pump M.TECH DISSERTATION (TURBOMACHINE)
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A shaft seal, e.g. a stuffing box or a mechanical seal, prevents the liquid from escaping into the environment environment or the bearing housing. housing. Impeller and casing are separated by a narrow annular seal through which some leakage flows back from the impeller outlet to the inlet. A second annular seal on the rear shroud serves the purpose of counterbalancing the axial forces acting on the impeller front and rear shrouds. The leakage through this seal flows back into the suction chamber through axial thrust balance hole which are drilled in hole. The impeller can be described by the hub, the rear shroud, the blades transferring energy to the fluid and the front shroud. In some applications the front shroud is omitted. In this case
the impeller is termed “semi -open”. The leading face of the blade of the rotating impeller experiences the highest pressure for a given radius. It is called pressure surface or pressure side. The opposite blade surface with the lower pressure accordingly is the suction surface or suction side. When looking into the impeller eye we see the suction surface. Therefore, it is sometimes
called the “visible blade face” or the “lower blade face”, whilst the pressure surface, not visible from the impeller eye, is called the “upper blade face”.
Fig 1.2 Meridonial and plan view of impeller
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A shaft seal, e.g. a stuffing box or a mechanical seal, prevents the liquid from escaping into the environment environment or the bearing housing. housing. Impeller and casing are separated by a narrow annular seal through which some leakage flows back from the impeller outlet to the inlet. A second annular seal on the rear shroud serves the purpose of counterbalancing the axial forces acting on the impeller front and rear shrouds. The leakage through this seal flows back into the suction chamber through axial thrust balance hole which are drilled in hole. The impeller can be described by the hub, the rear shroud, the blades transferring energy to the fluid and the front shroud. In some applications the front shroud is omitted. In this case
the impeller is termed “semi -open”. The leading face of the blade of the rotating impeller experiences the highest pressure for a given radius. It is called pressure surface or pressure side. The opposite blade surface with the lower pressure accordingly is the suction surface or suction side. When looking into the impeller eye we see the suction surface. Therefore, it is sometimes
called the “visible blade face” or the “lower blade face”, whilst the pressure surface, not visible from the impeller eye, is called the “upper blade face”.
Fig 1.2 Meridonial and plan view of impeller
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1.3 Types of centrifugal pump Centrifugal Pumps are classified into t hree general categories:
•
Radial flow – a centrifugal pump in which the pressure is developed wholly by
centrifugal force.
•
Semi-axial – a centrifugal pimp in which the pressure is developed by centrifugal
force partly by the lift of t he vanes of the impeller on the liquid.
•
Axial flow – a centrifugal pump in which the pressure is developed by the propelling
or lifting action of the vanes of the impeller on the liquid.
Fig. 1.3 Types of impeller
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1.4 Performance characteristics Due to need of variable operational requirements, practically all pumps temporarily operate
away from the design point which is defined by q* ≡ Q/Qopt = 1. Overload corresponds to q* > 1, while operation at q* < 1 is called “partload”.
The pump characteristics describe the
behavior of head, power consumption and efficiency as functions of the flow rate.
The characteristics are measured on the test stand by throttling the discharge valve in order to obtain different flow rates corresponding to the valve openings. At a given speed, unique values of head and power are established at every specific flow rate. The resulting curve H = f (Q) is called
“head -capacity curve” or “Q -H-curve”.
1.4.1. Theoretical characteristics
The expression of theoretical head developed by centrifugal pump can be written from
Euler’s equation in this way:
Where D = outer diameter of impeller N = Rotational speed A = the flow area at t he periphery of the impeller
β2 = outlet blade angle of the impeller From the above equation it can be seen that for a given impeller only H theo t heo and Q are the variable, so we can write above equation equat ion in this way H theo t heo = K 1 - K 2 2 Q
Therefore head and discharge bears a linear linear relationship, so H-Q curve is a straight line line and at zero flow K 1 is the head developed by the impeller. This is shown in figure 1.4
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Fig 1.4 Theoretical head discharge characteristics 1.4.2. Actual characteristics
The actual characteristic is obtained by deducting losses from theoretical head. Hence Hactual =
Htheoretical - losses
So for actual characteristics it is required to know about the losses.
Fig 1.5 Actual head discharge characteristics
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The shape of these performance curves over the range from shut-off (or zero flow Q = 0) to the maximum possible flow rate is important for the operational behaviour of the pump in the plant. The majority of applications require a Q-H-curve steadily falling with increasing flow rate,
i.e. ∂H/∂Q < 0. This is termed a “ stable characteristic ”. In contrast, if the Q -H-curve has a range with ∂H/∂Q > 0, the characteristic is said to be “ unstable”. Unstable or flat Q -H-curves can cause problems in parallel operation or with a flat system characteristic.
Fig 1.6 Pump performance curve Best efficiency point: It is defined as a point on H-Q curve for the flow capacity at which
efficiency is maximum. When operating a pump it is recommended that the pump be sized to run as close to the BEP as the application allows.
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CHAPTER 2 (LOSSES IN CENTRIFUGAL PUMP) INTRODUCTION
As described in previous section Euler’s pump equation provides a simple, loss free description of the impeller performance. In reality, because of a number of mechanical and hydraulic losses in impeller and pump casing, the pump performance is lower than predicted by the Euler pump equation. The losses cause smaller head than the theoretical and higher power consumption, the result is a reduction in efficiency. A study of losses in centrifugal pump may be undertaken one of the following reasons: 1. To know the actual characteristics from theoretical characteristics it is required to deduct the loss head from theoretical head. 2. Information about the nature and magnitude of losses may indicate the way to reduce these losses. 3. If the losses are known, it is possible to predetermine the head-capacity curve of a new pump by first assuming or establishing in some other manner the head -capacity curve of an idealized pump. 4. Pump performance curves can be predicted by means of theoretical or empirical calculation models for each single type of loss. Accordance with the actual performance
curves depends on the models’ degree of detail and to what extent they describe the actual pump type.
2.1 Types of losses in centrifugal pump: In centrifugal pump there are basically two types of losses hydraulic and mechanical which can be divided in number of sub groups which are listed as below: Disk friction losses Losses through annular seal Incidence loss Friction loss Mixing loss Recirculation loss Mechanical loss
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2.1.1 Disk friction losses
When a circular disk or a cylinder rotates in a fluid, shear stresses corresponding to the local friction coefficient cf occur on its surface, On a disk rotating in an extended stationary fluid
(without the influence of a casing) the shear stress is τ = ½ρ×cf×u2 with u = ω×R. The friction force on a surface element dA = 2π×r×dr is then dF = 2π×τ×r×dr and the torque exercised
by friction becomes: dM = r×dF = π×ρ×cf×ω2×r4×dr. The friction power per side
of the disk PRR = ω×M is obtained from the integral PRR = ω×∫dM (between inner radius r1 and outer radius r2) as PRR = (π/5)×ρ×cf×ω 3×r 2 5×(1 - r 15/r 25). The friction coefficient cf depends on the Reynolds number and the sur face roughness.
Fig. 2.1 Disk friction on impeller
If the body rotates in a casing (as is the case in a pump) the velocity distribution between casing and rotating body depends on the distance between the impeller shroud and the casing wall as well as on the boundary layers which form on the stationary and rotating surfaces. A
core flow with approximately cu = ½ω×r is obtained (in other words, u = ω×r can no longer be assumed). In the case of turbulent flow the power absorbed by a disk in a casing therefore amounts to roughly half of the power of a free disk rotating in a stationary fluid.
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The disk friction losses depend on the following parameters: Reynolds number Roughness of the rotating disk Roughness of the casing wall Axial side wall gap Shape of the casing and size of the impeller side wall gap Influencing the boundary layer Leakage flow Exchange of momentum
2.1.2 Leakage loss through annular seals
The annular seal consists of a case ring and a rotating inner cylinder. The clearance s between the rings is small compared to the radius of the rotating parts (s << r sp). Due to the pressure difference across the seal, an axial flow velocity c ax is generated. With the rotor at rest, this axial flow can be treated according to the laws of channel flow if the hydraulic diameter dh = 2×s is used. Any leakage reduces the pump efficiency. Since the entire mechanical energy transferred by the impeller to the leakage flow (i.e. the increase of the static head and the kinetic energy) is throttled in the seal and converted into heat, one percent of leakage flow also means an efficiency loss of one percent. Through the rotation of the inner cylinder a circumferential flow is superimposed on the axial flow. To describe these flow conditions two Reynolds numbers are required: Re for the axial and Reu for the circumferential flow.
Fig. 2.2 Leakage flows: a) multistage pump; b) impeller with balance holes; c) double entry impeller M.TECH DISSERTATION (TURBOMACHINE)
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2.1.2.1 calculation procedure for leakage loss
To start with, the pressure difference acting over the seal must be established. The static pressure H p prevailing at the impeller outlet can be calculated from
In most cases H p can be estimated accurately enough with the help of the degree of reaction H p = RG×H. For low and moderate specific speeds R G = 0.75 is a good assumption. With radially inward directed leakages (Qs1 and Qs2 in Fig. ) the pressure between the impeller outlet and the seal drops in accordance with the rotation of the fluid in the impeller sidewall
gap . This is described by the rotation factor k = β/ω (β is the angular velocity of the fluid). As per Eq
The pressure reduction in the impeller sidewall gap can be calculated from Δp = ½ρ×β 2×(r 22 - r sp2)
= ½ρ×k 2×u22×(1 - dsp*2). For determining the pressure difference over the seal at the
impeller inlet we use equation:
The greater the fluid rotation (i.e. the greater k) the greater is the pressure drop in the sidewall gap and the smaller is the pressure difference over the seal and the resulting leakage flow. Since k increases with growing leakage a radially inward leakage depends on itself and partly limits itself. 2.1.3 Incidence losses
Incidence loss occurs when there is a difference between the flow angle and blade angle at the impeller or guide vane leading edges. This is typically, the case at part load or when prerotation exists. M.TECH DISSERTATION (TURBOMACHINE)
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Fig. 2.3 Incidence loss as function of flow A recirculation zone occurs on one side of the blade when there is difference between the flow angle and the blade angle, see Figure. The recirculation zone causes a flow contraction after the blade leading edge. The flow must once again decelerate after the contraction to fill the entire blade channel and mixing loss occurs. At off-design flow, incidence losses also occur at the volute tongue. The designer must therefore make sure that flow angles and blade angles match each other so the incidence loss can minimized. Rounding blade edges and volute casing tongue can reduce the incidence loss.
Fig. 2.4 Velocity triangle at impeller inlet M.TECH DISSERTATION (TURBOMACHINE)
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2.1.4 Friction loss
Flow friction occurs where the fluid is in contact with the rotating impeller surfaces and the interior surfaces in the pump casing. The flow friction causes a pressure loss which reduces the head. The magnitude of the friction loss depends on the roughness of the surface and the fluid velocity relative to the surface.
Fig. 2.5 Frictional head loss as a function of velocit y 2.1.5 Mixing Losses or Losses due to vortex dissipation
While static pressure can be converted into kinetic energy without a major loss (accelerated flow), the reverse process of converting kinetic energy into static pressure involves far greater losses. The reason for this is that in real flows the velocity distributions are mostly nonuniform and subject to further distortion upon deceleration. Non-uniform flow generates losses by turbulent dissipation through exchange of momentum between the streamlines. Such pressure losses are called “form” or “mixing” losses.
Fig.2.6 Mixing loss
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2.1.6 Recirculation Losses
Recirculation zones in the hydraulic components typically occur at part load when the flow is below the design flow. Figure shows an example of recirculation in the impeller. The recirculation zones reduce the effective cross-section area which the flow experiences. High velocity gradients Occurs in the flow between the main flow which has high velocity and the eddies which have a velocity close to zero. The result is a considerable mixing loss. Recirculation zones can occur in inlet, impeller, return channel or volute casing. The extent of the zones depends on geometry and operating point. When designing hydraulic components, it is important to minimise the size of the recirculation zones in the primary operating points.
Fig. 2.7 Recirculation loss in impeller 2.1.7 Mechanical losses
The mechanical losses Pm are generated by the radial bearings, the axial bearing and the shaft seals. Occasionally Pm includes auxiliary equipment driven by the pump shaft. These losses depend on the design of the pump, i.e. on the selection of anti-friction versus journal bearings or stuffing boxes versus mechanical seals. Generally mechanical losses found by documentation of the manufacturer of t he pump.
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CHAPTER 3 (LOSS MODELS) 3.1 Different Models Used To Calculate Losses:
The four different Models proposed by different authors are used to calculate the losses in the centrifugal pump, in this analysis. 1. Tuzson`s Method 2. Gulich`s Model 3. Church`s Model 4. Stepanoff`s Model 3.1.1 Tuzson Model [5]:
Tuzson proposed model to calculate different types of losses in pumps. He tried to give simple and fast procedure with minimum inputs requirements. Tuzson considers the following hydraulic losses for the calculating of losses (1) Incidence losses, (2) skin friction losses, (3) Volute head loss, (4) Diffusion loss and (5) Diffuser loss.
3.1.1.1 Theoretical Hydraulic Head:
Theoretical Hydraulic Head is given by H th
[3-1]
3.1.1.2 Impeller Incidence Losses:
Incidence Losses at the pump inlet are calculated by assuming a leading-edge separation, and a sudden expansion loss, when the separated flow mixes. Calculation of the extent of the separated region and the corresponding velocity increases follows a potential flow model, solved by conformal transformation. It is assumed that the loss is proportional to the square of the difference between the tangential component of the inlet velocity and the circumferential velocity. The calculation of inlet incidence loss does not include any empirical loss coefficient. Assumption taken in this calculation is a radial leading edge a nd an axial inlet velocity.
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[3-2]
3.1.1.3 Volute Head Loss:
It results from a mismatch of the velocity leaving the impeller and the velocity in the volute throat. If the velocity approaching the volute throat is larger t han the velocity at the throat, the velocity head difference is lost. The velocity approaching the volute throat can be calculated by assuming that the velocity leaving the impeller decreases in proportion to the radius because of the conservation of angular momentum.
( )
[3-3]
3.1.1.4 Skin-Friction Losses:
This loss in the impeller and diffuser or volute follows the standard pipe friction model. Since the flow passage cross-section is irregular, a hydraulic radius and average flow velocities are used. The friction coefficient can be adjusted but has a default value of 0.005. The hydraulic radius of the impeller blade is obtained by dividing the passage cross sectional area by half of the circumference. Hydraulic radius of the impeller passage Is given by:
[3-3]
Impeller skin friction loss is given by:
] [⁄⁄⁄
[3-4]
Volute skin friction loss is given by:
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√
[3-5]
Diffuser skin friction loss is given by:
√
[3-6]
3.1.1.5 Diffusion Loss:
This loss needs to be taken into account, since separation invariably appears in the impeller at some point. The program assumes that when the ratio of the relative velocity at the inlet to the outlet exceeds a value of 1.4 of the velocity head difference is lost.
[3-7]
3.1.1.6 Diffuser Loss:
To calculate the diffuser loss the program estimates the pressure recovery coefficient based on the area ratio and applies an adjustable loss coefficient. In pumps the diffuser accounts for the greatest head loss, much influenced by the detailed design of the diffuser. Therefore, estimating diffuser losses is particularly difficult. Some designers assume, as a rule of thumb, that half of the diffuser inlet head is lost.
3.1.2
[3-8]
Gulich Model [11]:
Gulich presents the model for the losses in the various component of the centrifugal pump, like impeller, volute and diffuser. Hydraulic efficiency calculated from the power balance does not give any information about the contribution of the losses individual pump components. To answer this question, it is useful to estimate the loss in individual components. Such calculations have an empirical character since the three-dimensional
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velocity distributions in the impeller and diffusing elements, which determine both friction and turbulence losses, cannot be described by simple models. Estimations of this type are only meaningful near the best efficiency point. Gulich gives the co relations for the co efficient of the various losses in the various component of the centrifugal pump. 3.1.2.1 Loss Model for Impeller:
The loss co efficient for the impeller can be given by:
[3-9]
This co relation includes the frictional and mixing losses and the shock loss co efficient. The co relation for the frictional and mixing loss co efficient is given by:
[3-10]
Where, Cd is the dissipation co efficient. The dissipation co efficient ( C d ) can be calculate from the friction co efficient by adding 0.0015 and the value obtained in this way is further multiplied by an empirical factor containing the relative impeller outlet width. The empirical factor can thus be interpreted as the effect of uneven velocity distributions and secondary flow.
( )
[3-11]
Where, C f is the co efficient of friction.
{}
[3-12]
It is possible to estimate the shock losses at the impeller inlet. The co relation for the shock loss is given by:
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This equation describes the deceleration of the vector of the mean inflow velocity w 1m (from the velocity triangle) to the velocity w 1q in the throat area A1q. This relationship should not be used for w1q/w1m < 0.6. 3.1.2.2 Loss Model for Diffuser:
Co efficient for the losses in the diffuser is given by:
Where,
is the friction loss in the inlet region, the co efficient
[3-14]
is the co-efficient for
the over flow channel or return channel and the C p is the pressure recovery co efficient, which is the function of the area ratio and the ratio of the length of the blade and the radius,
. The value of the C p can be found out from the graph. Term
describes the actual flow deceleration.
Fig. 3.1 Pressure Recovery Co efficient C p M.TECH DISSERTATION (TURBOMACHINE)
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The friction losses between the impeller outlet and the diffuser throat area can be estimated by calculating the energy dissipated through wall shear stresses on the blades and the sidewalls, which is given by:
( )
[3-15]
3.1.2.3 Loss Model for Volute:
In the calculation for the losses in the volute casing, Gulich had not considered the mixing losses due to an inflow with a non-uniform velocity profile. The co relation for the hydraulic loss in the volute is:
[3-16]
The co relation given by Gulich to finding out the losses in the volute consist the friction loss, loss in discharge nozzle and the shock loss. The friction loss in the volute casing can calculate by:
∑( )
[3-17]
Where, ∆ A is wetted surface. The diffuser or the pressure or discharge nozzle follows the actual volute. The losses in the discharge nozzle can calculate by:
[3-18]
The pressure recovery co efficient C p can calculate as above in the diffuser losses calculation. The shock loss in the impeller obtained is also occurs in the volute casing. In the case of diffusers, the expansion from b 2 to b3 is implicitly included in Eq. (3-20). The effect of blade
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blockage can be considered in a similar way as in volute. The shock loss co efficient in the volute is given by:
Where ⱷ2 is the flow co efficient, and
[3-19]
τ 2
is the blade blockage.
The flow co efficient can calculate by:
[3-20]
The blade blockage can calculate by:
3.1.3
[3-21]
Stepanoff Model [12]:
Stepanoff proposed a model to calculate the hydraulic losses in the centrifugal pump. He discussed the general model without considering losses in the individual parts of the centrifugal pump. He considers mainly two losses so called skin friction loss and the eddy and separation loss, which are includes the shock loss and diffusion loss. 3.1.3.1 Friction and Diffusion Losses:
The friction loss in the pump can be calculating with the use of one of the general formula. It can be given by:
[3-22]
This formula can be use for assuming the several paths in the pump. It can be apply to the pump by dividing t he total passage of the pump in the several passage of every component like impeller channel, volute, diffuser or discharge nozzle. However, because of the difficulty in the determining the actual path length and the hydraulic radius its very complicated method to determine the frictional loss in pump. Selection of the co efficient of the friction is also the difficult task. Therefore, for facing these types of the difficulty, it is a better idea to
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use one simple and easy equation to calculate the losses. For this reason, various investigators combine the all-frictional losses into a single formula by simplified it which can be given as:
[3-23]
Where, k 1 is the constant for the frictional loss for a given pump. This constant covers all lengths, areas and area ratio, friction co efficient and other unknown factors affecting the frictional head loss. It also includes any error caused by inability to find the better expression for several items contributing to the frict ion losses. In the case of the diffusion loss, also simplify the expression. The diffusion loss in the impeller channel and discharge nozzle stated by:
[3-24]
Where, k difn is the constant for the diffusion loss. Which also covers all thing affect the diffusion loss. It ca seen from the both the equation of the friction loss and the diffusion loss, that the both the losses are vary with the square of the velocity. Therefore, they can be combined into one equation. The combine equation for the friction and diffusion loss can be given by:
[3-25]
Where, k fd is the co efficient for the friction and diffusion loss.
3.1.3.2 Eddy and Separation Losses:
Stepanoff considers eddy and separation loss as a shock loss. When liquid enters at impeller entrance at high angle of attack, loss appears, the reason for it is that the sudden expansion or diffusion after separation. He also considers the loss at the impeller discharge. At the impeller discharge loss often caused by a high rate of shear due to a low average velocity in the volute and high velocity the impeller discharge. At the BEP, the average velocity of the volute is considerably lower than the impeller discharge. There is a shock loss at the cutwater of the
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volute pump and the entrance of the diffusion vanes when a diffusion vane casing is used. The formula for the calculation for the shock loss is given by:
[3-26]
Where, k s , is the co efficient for the shock loss. In this formula, The term Qs is the shock less flow [3],[22], at where the direction of flow agrees with the vane angles at both entrance and discharge. Means at that point there is no additional loss occurring. It means that at the point above and below Qs, there will be a sudden change in the direction and magnitude of the velocity of the flow. 3.1.4
Church Model [13]:
Church considers that the losses occur in the pump system are due to the friction in passage and from the turbulence occur while passing through the obstruction, sudden change of the section in the pump. 3.1.4.1 Friction Loss:
For the friction losses in the centrifugal pump, Church have accepts one most general formula to calculate the friction losses. The Darcy equation is used to calculating the friction losses in the pump system. Darcy equation is given by:
[3-27]
Where, f is an empirical co efficient depends upon the Reynolds number. Moreover, the L/d ratio is the dimension less, so any consistent units may be used for L and d. if the passage is not circular or if it had an annular shape the hydraulic radius may be used in place of the diameter d in circulating the Reynolds number and in the Darcy equation. In this way, Darcy equation can be present as:
[3-28]
Where, Rh is the hydraulic radius of the passage. This equation can be use for the passages between the impeller, volute and the discharge nozzle [3]. Since the shape of the impeller passage and the volute is not straight, we can find the losses, considering the series of the short path of the passages. M.TECH DISSERTATION (TURBOMACHINE)
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3.1.4.2 Turbulence Loss:
In the pump, the flow is always turbulent. At certain section in this machine, such as at the inlet and outlet edge of the vanes in both the impeller vanes etc. the flow is seriously disturbed with a resultant loss of head. These losses are also known as shock losses. This loss is the proportional to the square of the velocity. Its co efficient is quite difficult to determine. A pump is designed for a given flow and speed at which it is expected to operate most of time. The angles of the impeller and diffuser vanes are designed for these conditions. When operating at the other flow and speeds, these angles will not be correct and the turbulence losses will increase. Sudden change in the section and sharp turns should be avoided or minimized, as much as possible. The very well known loss formula for t he calculation of the shock loss given by Stepanoff [0]
can be used in the loss calculation in Church’s model. The formula given by the Stepanoff for the calculation of the shock loss i s:
[3-29]
Where, k s is the co efficient for the shock loss and Q s is the shock less flow.
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CHAPTER 4 (LITERATURE REVIEW) Ali nemdili, Dieter-Heinz Hellmann[1] deals with experimental investigations on fluid
friction of rotational discs in real centrifugal pump casings. To evaluate the disc friction experiments are conducted without the assembly of the disc and without filling the pump with water for various values of the rotational speed in order to obtain the mechanical power due to bearing- and mechanical seal frictions. The influence of the diffuser device will be investigated through the inset of three different volutes. The rotational speed will be varied by means of an electronic hand-adjustable speed control integrated in the motor. Afterward Experiments are conducted with water. The purpose of the investigations reported here is to develop an improved empirical equation by examining discs with different geometrical parameters running in a real centrifugal pump volute casing of different width. The results show that the disc friction loss depends strongly on the axial gap, on the Reynolds number, on the surface roughness and on the width of the volute. By dimensional analysis he give an empirical relation for disc friction losses with high accuracy. Khin Cho Thin, Mya Mya Khaing, and Khin Maung[2] predict the performance of the
pump by using
deals with the design and performance analysis of centrifugal pump. They
analysed centrifugal pump by using a single-stage end suction centrifugal pump. A design of centrifugal pump is carried out and analysed to get the best performance point. They designed the dimensions of the centrifugal pump and then the analysis of centrifugal pump is carried out. Shock losses, impeller friction losses, volute friction losses, disk friction losses and recirculation losses of centrifugal pump are also considered in performance analysis of centrifugal pump. The low specific speed is chosen because the value of specific speed is 100. They show some loses of centrifugal pump with the values, Q and H is determined for the various operating points. Centrifugal pumps are fluid-kinetic machines designed for power increase within a rotating impeller. In centrifugal pumps, the delivery head depends on the flow rate, which is called pump performance, is illustrated by curves. To get characteristic curve of a centrifugal pump, values of theoretical head, slip, shock losses, recirculation losses and other friction losses are calculated by varying volume flow rate. Khalid. S. Rababa[3] investigate the effects of blade number on flow field and
characteristics of a centrifugal pump. Three models of impellers were used with 2, 3 and 4 blades. Two of these models having 3 blades with additional short blades and t he third model also having 3 blades but with an increment in blade thickness of outlet part (channel form). M.TECH DISSERTATION (TURBOMACHINE)
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The geometrical profile of impeller blades was identical. The same volute is used for all three configuration. The inner flow fields and characteristics of the centrifugal pump with different blade number and shape are simulated and, the comparison between prediction values and experimental results indicates that the prediction results are satisfied. From experimental results it is found that with increasing of blade number, the optimal pump discharge shifts to
the right, and increases pump pressure head H and efficiency η. For impeller with additional short blades between the main blades H
increased by 1M (4%), and η by (1%), it should be
noted that the length of the additional short blades by 1/3 or 2/3 of the main blade length, had
no effect on the characteristic curve Η −Q . Mohamad Memardezfouli and Ahmad Nourbakhsh[4] In their
work, the slip
phenomenon at the impeller outlet is studied experimentally for five industrial pumps at different flow rates and the slip factor is estimated for each of these cases. Theoretical slip factors are calculated using several existing methods taking into consideration the main geometric parameters of the impeller. Then the experimental slip factors are compared with the calculated theoretical values. They investigate the influence of flow parameters on the slip factor and to obtain the effective value of slip factor for off-design conditions. After measuring experimental data, the real slip factor under any working conditions is calculated (from the experimental results) by introducing a distortion coefficient. The distortion factor validity range is not yet fixed due to the limited number of tested impellers and few detailed measurements of impeller outlet flow. Theoretical and experimental models were investigated to know about relationship between effective slip factor and flow rate in impellers and their relation to velocity distribution. John Tuzson [5] proposed method to calculate the performance of the centrifugal pump. A
simple and fast calculation procedure with minimal input requirements are presented in the book. He gives different formulas to for calculate the losses occur in the centrifugal pump. He shows that skin friction and diffuser losses increase with the square of the flow rate and predominate at high flow rates. Therefore, the loss coefficient can be adjusted when the head deviates from the experiment data at high flow rate. Volute loss depends on the impeller exit velocity, which increases with decreasing flow rate. The incidence losses are often fictitious, and the inlet blade angles should be adjusted to achieve minimal losses at the design flow rate. The disk friction loss, recirculation loss, affect only the losses, which is also include the mechanical losses of the bearings, affect only the efficiency, not the head.
M.TECH DISSERTATION (TURBOMACHINE)
Page 25
VasiliosA. Grapsas, John s. anagnostopoulos and Dimitrios e. papantonis[6] has done
experimental and numerical investigation of a radial flow pump impeller with 2D curvature blade geometry. Investigation of the behaviour of the above impeller for a wide flow rate range and for various rotational speeds was carried out and the obtained experimental results were validated with available measurements of the same impeller within spiral casing. The flow field through the impeller was also simulated by a 2-dimensional approach. For the numerical simulation, the viscous Navier- Stokes equations are solved with the control volume approach and the k- ε
turbulence model. The flow domain is discretized with a polar,
unstructured, Cartesian mesh that covers periodically symmetric section of the impeller. Advanced numerical techniques for adaptive grid refinement and for the partially blocked cells are also implemented at the irregular boundaries of the blades. The numerical results are compared to the measurements, showing good agreement and encouraging the extension of the developed computation methodology for performance prediction and for design optimization of such impeller geometries. A numerical methodology for the calculation of the flow field in centrifugal pump impellers with 2D curvature is developed and validated against corresponding experimental data taken at a Laboratory test rig. The flow is calculated using a two dimensional approach in order to achieve a fast simulation and the agreement between the numerical results and the measurements is satisfactory. This is quite encouraging result in order to apply the present numerical model to further flow analysis, as well as, for design optimization purposes in these pump types.
U.S. Department of Energy’s Industrial Technologies Program (ITP) and the Hydraulic Institute (HI).[7] discussed about improving pump system performances. This section
describes the key components of a pumping system and opportunities to improve, the
system’s performance.in this he also describes key considerations in determining the life cycle costs of pumping systems. By using appropriate piping system, prime movers, valves, heat exchanger, we can improve system performance. This section also deals with maintenance of pumping system such as bearing replacement; wear ring clearances, mechanical seal replacement. Certain problems must be prevented, such as cavitation, internal recirculation, seal or packing wear, poor material selection, and improper shaft loading.
MarioŠavar, Hrvoje Kozmar a, IgorSutlović[8] experimentally investigates the effect on the efficiency of centrifugal pump by impeller trimming. This idea is based on affinity laws that say pump impellers are considered to be similar if they satisfy geometric and kinematic M.TECH DISSERTATION (TURBOMACHINE)
Page 26
similarity conditions. After the pump impeller has been trimmed, geometric and kinematic similarity conditions were not completely preserved. In this paper, the influence of disregarded similarity after impeller trimming is examined. For the purpose of this experiment, the impeller was trimmed seven times successively diminishing the outlet diameter by a 10 mm step. The experiment was accomplished on a low specific speed centrifugal pump. The obtained results are presented in non- dimensional
form in a ψ−φ
diagram. According to affinity law efficiency line should remain the same for the series of trimmed impellers. In Fig. 8 a series of efficiency lines is depicted and a good adherence can be noted for diameters 190 and 180 mm and even for 170 mm. As amount trimmed increases i.e. as impeller diameter becomes smaller efficiency deteriorates significantly. The main reason for this could be growing the gap between the impeller . P. thanapandi and Rama prasad [9] theoretically and experimentally investigate on the
transient characteristics of a centrifugal pump during starting and stopping periods. Experiments have been conducted on a volute pump with different valve openings to study the dynamic behaviour of the pump during normal start up and stopping, when a small length of discharge pipe line is connected to discharge flange of the pump. Similar experiments have also been conducted when the test pump was part of a hydraulic system to study the system effect on the transient characteristics. Instantaneous rotational speed, flow rate, and delivery and suction pressures of the pump are recorded and it is observed in all the tested cases that the change of pump behaviour during the transient period is quasi-steady. The dynamic characteristics of the pump have been analysed by a numerical model using the method of characteristics. The model is presented and the results are compared with the experimental data. As the model contains speed acceleration and unsteady discharge terms, the model can be applied for analyses of purely unsteady cases where the pump dynamic characteristics show considerable departure from their steady-state characteristics. It is observed in all the tested cases that the transient head characteristics closely follow the steady-state system head curve and the change of operating point during normal starting and stopping transients is quasi-steady. The dynamic characteristics of the test pump have been analysed by a numerical model using the method of characteristics. The model predicts well the trend of the dynamic head characteristics during transients. The method can be extended to the analysis of purely unsteady cases, where the pump operation is no more quasi-steady. Craig I. Walker, Greg C. Bodkin[10] predicts the wear rate on slurry pump inlet side-liners.
Experimental work has been conducted on different slurry pump impeller and side-liner M.TECH DISSERTATION (TURBOMACHINE)
Page 27
geometries to determine the effects of solid particle size, slurry concentration and pump speed on wear. The side-liner material used has the Brinell Hardness Number of 110-ASTM E10-66. To ensure a reasonably fast wear rate. Pump hydraulic shape was varied from the original test on the standard heavy duty STD. impeller with the objective of comparing different impeller styles with the same side-liner as well as different side-liners with similar impeller styles. For the tests here the wear rates have been determined from cumulative wear depth at the deepest point, against the cumulative tonnes pumped i.e. mm/kT. The rate was calculated as the average slope of a straight line through the data points excluding the origin. From the obtained graph they found (1) the wear rate for the HE design varies with the square of the particle size.(2) the wear rate for the STD and RE designs did not vary significantly with particle size.(3) the wear rate was constant for varying solids concentration(4) the wear rate was constant for varying impeller tip speed. Johann Friedrich Gulich [11] proposes method for the losses occur in the centr ifugal pump.
Formulae are given to determine the co efficient for the hydraulic losses, disk friction loss, leakage in radial gap, open impeller, in annular seal were given. For the hydraulic losses calculations, the formulae for the individual pump component given in this book, like the impeller, volute with discharge nozzle and diffuser. Gulich has also proposed some steps to reduce these losses and improve the efficiency of the pump.
A. J. Stepanoff [12] suggests the method for finding out different losses occur in the centrifugal
pump. Stepanoff considers the friction loss and eddy and separation loss, which affect the head of the centrifugal pump. He considers eddy and separation loss as shock loss. He gives formula to find out the losses. He also investigates the leakage loss, disk friction loss and mechanical loss. The author also has calculated the leakage loss for a number of double suction horizontally split pumps of different specific speeds and the in the results it will be observed that leakage loss decreases with increasing specific speed. The disk friction loss was computed for a number of double suction pumps. This loss expressed as percentage of pumps of different specific speeds. The rapid rise of the disk friction loss at specific speeds, below 2000. The entire range of specific speeds, leakage loss is approximately equal to one half of the disk friction loss. Austine A. Church [13] proposed a method to find different losses in centrifugal pump.
Author gives formulas for finding out the loss of head due to turbulent or shock loss and M.TECH DISSERTATION (TURBOMACHINE)
Page 28
friction, disk friction and leakage loss . He show that the friction loss increases with the square of the flow. The losses also increase with the wetted area of the passages, so they should be kept as small as possible. It increases with the roughness of the surface of the impeller, diffuser or volute or casing passages. The turbulent loss is depending upon the angles of the impeller and diffuser vanes. The turbulent loss will increase if these angles are not correct. Sudden change in the section or the sharp change turn should be avoided.
M.TECH DISSERTATION (TURBOMACHINE)
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CHAPTER 5 (EXPERIMENTAL STUDY)
5.1 INTRODUCTION For getting actual performances of the given pump (KDS1030++) we have perform test on our fluid lab. We have also participated in developing of that test rig for forward mode. The experimental part of our study includes following discussion. Overview of the test rig Experimental procedure Pump specification Measurement of variables Results
5.2 Overview of the test rig A compact open loop-test rig was used for testing the pumps in normal mode. Schematic diagram of test-rig is shown in Figure 4.1. The test rig consists a base frame which can accommodate the pump of radial flow type for testing, which provide required flow and head for testing pump at fixed rotational speed. From sump, water is passed to suction side of pump through foot valve and concentric reducer where suction pressure gets measured by vacuum transducer and shown digitally in meter. At discharge high pressure water passes to tank through flow meter. At discharge output pressure gets measured by pressure transducer and shown digitally in meter. And flow meter gives flow digitally in meter. The schematic of the setup employed for testing the centrifugal pump is given in the figure 5.1 The motor of the pump is connected with variable frequency drive (VFD) to change the speed of the pump. The delivery pipe is fitted with a regulating valve. The discharge of the pump is measured using a magnetic flow measurement. A pressure gauge is provided on a delivery side and vacuum gauge on suction side. A pipe with a valve is provided in the suction pipe for priming the pump. The centrifugal pump is driven by a constant speed torque reaction type alternative current motor which is driven by VFD(Variable frequency drive). VFD(Variable frequency drive) is the controllable unit for the motor-pump. Using this, speed of the motor from lower to higher (vice versa) can easily be done at no losses and over a wide
M.TECH DISSERTATION (TURBOMACHINE)
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range of speeds. Rotational speed of the impeller is measured by inductive proximity sensor. The pump with its drive motor is supported on a common platform.
Fig. 5.1 Test rig for normal mode 5.3 EXPERIMENTAL PROCEDURE FOR TEST READINGS The delivery pipe of pump is closed before starting the pump to allow the build-up of
pressure. Pump is primed properly by filling water in the suction pipe and the casing of the pump. Air is completely removed from the pump before it is run. The drive motor of the pump is run by switching on the variable frequency drive. Required pump speed is adjusted t hrough the variable frequency drive. The readings of the pressure transducer, vacuum transducer, pump speed, power input
and discharge may be noted. The flow rate is gradually increased by opening the delivery valve. The above
measurements may be noted for various flow rates. M.TECH DISSERTATION (TURBOMACHINE)
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The discharge in each case is measured using magnetic flow meter.
5.4 PUMP SPECIFICATION
Pump parameters Value given by manufacturer
Geometrical parameters measured
Value
Type
KDS 1030++
Outer diameter
158 mm
Head
25 m
Eye diameter
94 mm
Flow
22 lps
Hub diameter
68 mm
IPKW
8.42
Eye width
45mm
RPM
2900
Width of exit
20mm
Efficiency
64%
Inlet blade angle
19o
Head range
10 to 29 m
Outlet blade angle
23o
Flow range
33.5 to 151 lps
No of blade
6
Pump suction dia.
4 inch
Thickness blade
Pump dia.
4 inch
discharge
Motor
of
the
4.5 mm
3 phase ,50HZ,415V
Fig. 5.2 Pump specification
5.5 VARIABLE MEASURMENT Pressure measurement Flow measurement
Speed measurement
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5.5.1 PRESSURE MEASURMENT
For pressure measurement, Bourdon’s pressure gauge and the electronic pressure transducer were employed. The method of static pressure measurement is in accordance to the IEC prescribed standards with four diametrically opposite pressure-measuring tapping points. The static pressure at suction side of the pump is measured by vacuum transducer and at the delivery side of the pump is measured by electronics pressure transducer. Pressure gauges have also been used for manual measurement of the suction and delivery pressure.
Fig. 5.3 Pressure transducer and indicator
5.5.2 FLOW MEASUREMENT Flow through pipe at outlet of pump gets measured by magnetic flow meter, based on electromagnetic principal of working. One gate valve has been also installed after the magnetic flow meter to vary flow. Flow readings are shown digitally in indicator. Figure of flow meter has been shown in Fig. 5.4
M.TECH DISSERTATION (TURBOMACHINE)
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Fig. 5.4 Flow meter & indicator
5.5.3 SPEED MEASUREMENT Rotational speed of the impeller was measured by using Inductive proximity sensor. An inductive proximity sensor is a non-contact device that is used to detect a metal target. When
power is applied to an inductive proximity sensor the sensor’s coil will generate an oscillating electromagnetic field out of the face of the sensor. When the metal target gets close enough to
the sensor’s face it begins to penetrate the electromagnetic field. When this happens, eddy currents are generated on the surface of the metal target. As the metal target gets closer to the sensor face, the eddy currents increase which in turn decrease the amplitude of the
electromagnetic field. Once the electromagnetic field’s amplitude is reduced to a certain level, the sensor will activate indicating it has detected the metal target. In this setup, bolt is mounted on a flange which is sensed by proximity switc h which in turn is converted in digital signal and speed is displayed on speed indicator .
M.TECH DISSERTATION (TURBOMACHINE)
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Fig. 5.5 Proximity sensor & indicator 5.6 RESULTS AND DISCUSSION We have perform trial on KDS1030++ for normal mode at different constant speed 2900,2200,1500,1300 and 1100 rpm, and plot head developed ,efficiency and power input with respect to discharge. The obtain performance curves are approximately close matching with actual curves. Here the compound graphs for different speed for single variable with respect to discharge are shown. The corresponding reading for each speed has given in appendix.
M.TECH DISSERTATION (TURBOMACHINE)
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HEAD v/s FLOW OF KDS 1030++ PUMP 35
30
25
) 20 m ( D A E H15
2900 rpm 2200 rpm 1500 rpm 1300 rpm 1100 rpm
10
5
0 0
5
10
15
20
25
30
35
FLOW (l/s)
Fig. 5.6 Head vs discharge for different speed
M.TECH DISSERTATION (TURBOMACHINE)
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POWER v/s FLOW OF KDS 1030++ PUMP 9 8 7 6
) W5 K ( R E W4 O P
2900 rpm 2200 rpm 1500 rpm 1300 rpm
3
1100 rpm 2 1 0 0
5
10
15
20
25
30
35
FLOW (l/s)
Fig.5.7 Power vs discharge for different speeds
EFFICIENCY v/s FLOW OF KDS 1030++ PUMP 80 70 60
Y50 C N E I 40 C I F F E 30
2900 rpm 2200 rpm 1500 rpm 1300 rpm
20
1100 rpm
10 0 0
5
10
15
20
25
30
35
FLOW (l/s)
Fig. 5.8 Efficiency vs discharge for different speed M.TECH DISSERTATION (TURBOMACHINE)
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5.7 FUTURE WORK
It has been planned to apply different loss models on the selected pumps of different specific speed and to verify the result of these loss models with the result from the experimental work.
M.TECH DISSERTATION (TURBOMACHINE)
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APPENDIX – A FLO P suction P suction SR. Flow P Discharge P discharge Power In W (Kg/Cm2 (m of NO. (m3/s) (Kg/Cm2) (m of water) (KW) (lps) ) water) 1
0
-0.204
-2.04
0.24
2.4
0.331
1100
0
0
4.44
2 0.51 0.00051 -0.205
-2.05
0.24
2.4
0.342
1100
0.062934
0.062934
4.45
0.0222638 6.50988158
3 1.027 0.00103 -0.206
-2.06
0.24
2.4
0.36
1100
0.1267318 0.1267318
4.46
0.04493392 12.4816445
4 1.52 0.00152 -0.207
-2.07
0.239
2.39
0.372
1100
0.187568
0.187568
4.46
0.06650395 17.8774065
5 2.034 0.00203 -0.208
-2.08
0.238
2.38
0.389
1100
0.2509956 0.2509956
4.46
0.08899279 22.8773235
6 2.502 0.0025 -0.209
-2.09
0.236
2.36
0.399
1100
0.3087468 0.3087468
4.45
0.10922356 27.3743256
7
-0.21
-2.1
0.234
2.34
0.416
1100
0.3715574
0.3715574
4.44
0.1311483 31.526039
8 3.501 0.0035 -0.211
-2.11
0.232
2.32
0.426
1100
0.4320234 0.4320234
4.43
0.15214751 35.7153775
9 4.049 0.00405 -0.211
-2.11
0.23
2.3
0.445
1100
0.4996466 0.4996466
4.41
0.17516824 39.3636501
10 4.51 0.00451 -0.211
-2.11
0.228
2.28
0.453
1100
0.556534
0.556534
4.39
0.19422721 42.8757636
11 5.018 0.00502 -0.212
-2.12
0.225
2.25
0.468
1100
0.6192212 0.6192212
4.37
0.21512015 45.965845
12 5.502 0.0055 -0.212
-2.12
0.222
2.22
0.476
1100
0.6789468 0.6789468
4.34
0.23424985 49.2121535
13 6.012 0.00601 -0.212
-2.12
0.217
2.17
0.491
1100
0.7418808 0.7418808
4.29
0.25301442 51.5304315
14 6.501 0.0065 -0.213
-2.13
0.209
2.09
0.502
1100
0.8022234 0.8022234
4.22
0.2691297 53.6114937
15 6.807 0.00681 -0.213
-2.13
0.204
2.04
0.516
1100
0.8399838 0.8399838
4.17
0.27845871 53.964867
3.01
0
RPM
Velocity at Velocity at Total Head Power Out Suction Discharge Efficiency (m) (KW) (m/s) (m/s)
0.003
0
Fig. 5.9 Reading for 1100 rpm set
M.TECH DISSERTATION (TURBOMACHINE)
Page 39
0
APPENDIX – B
SR.NO.
FLOW (lps) Flow (m3/s)
P suction P suction (m P Discharge P discharge Power In (Kg/Cm2) of water) (Kg/Cm2) (m of water) (KW)
RPM
Velocity at Velocity at Total Head Power Out Suction Discharge (m) (KW) (m/s) (m/s) 0
Efficiency
1
0
0
-0.205
-2.05
0.403
4.03
0.444
1300
0
0
6.08
2
1.011
0.001011
-0.21
-2.1
0.401
4.01
0.468
1300
0.1247574
0.1247574
6.11
0.06059843 12.9483825
0
3
2.048
0.002048
-0.212
-2.12
0.398
3.98
0.534
1300
0.2527232
0.2527232
6.1
0.12255437 22.9502562
4
3.032
0.003032
-0.213
-2.13
0.394
3.94
0.558
1300
0.3741488
0.3741488
6.07
0.18054559 32.3558413
5
4.028
0.004028
-0.214
-2.14
0.389
3.89
0.594
1300
0.4970552
0.4970552
6.03
0.23827352 40.1133873
6
5.013
0.005013
-0.215
-2.15
0.382
3.82
0.654
1300
0.6186042
0.6186042
5.97
0.29358985 44.891415
7 8
5.013
0.005013
-0.215
-2.15
0.382
3.82
0.654
1300
0.6186042
0.6186042
5.97
0.29358985 44.891415
6.045
0.006045
-0.216
-2.16
0.375
3.75
0.672
1300
0.745953
0.745953
5.91
0.35047157 52.1535074
9
6.045
0.006045
-0.216
-2.16
0.374
3.74
0.672
1300
0.745953
0.745953
5.9
0.34987856 52.0652612
10
7.003
0.007003
-0.218
-2.18
0.36
3.6
0.708
1300
0.8641702
0.8641702
5.78
0.39708271 56.0851279
11
7.003
0.007003
-0.218
-2.18
0.359
3.59
0.708
1300
0.8641702
0.8641702
5.77
0.39639571 55.9880948
12
8.03
0.00803
-0.219
-2.19
0.343
3.43
0.738
1300
0.990902
0.990902
5.62
0.44271157 59.9880171
13
8.03
0.00803
-0.218
-2.18
0.343
3.43
0.783
1300
0.990902
0.990902
5.61
0.44192382 56.4398241
14
9.005
0.009005
-0.222
-2.22
0.312
3.12
0.762
1300
1.111217
1.111217
5.34
0.47173053 61.9068933
15
9.005
0.009005
-0.222
-2.22
0.312
3.12
0.762
1300
1.111217
1.111217
5.34
0.47173053 61.9068933
16
10.055
0.010055
-0.224
-2.24
0.279
2.79
0.78
1300
1.240787
1.240787
5.03
0.49615694 63.6098637
17
10.055
0.010055
-0.224
-2.24
0.279
2.79
0.78
1300
1.240787
1.240787
5.03
0.49615694 63.6098637
18
11.033
0.011033
-0.225
-2.25
0.238
2.38
0.798
1300
1.3614722
1.3614722
4.63
0.50112217 62.7972644
19
11.372
0.011372
-0.225
-2.25
0.222
2.22
0.798
1300
1.4033048
1.4033048
4.47
0.49867016 62.489995
Fig 5.10 Reading for 1300 rpm set
M.TECH DISSERTATION (TURBOMACHINE)
Page 40
APPENDIX – C SR.NO.
P suction P suction (m P D ischarge P discharge Power In FLOW (lps) Flow (m3/s) (Kg/Cm2) of water) (Kg/Cm2) (m of water) (KW)
1
0
0
-0.199
-1.99
2
1.033
0.001033
-0.203
-2.03
3
2.007
0.002007
-0.204
-2.04
4
3.057
0.003057
-0.207
-2.07
5
4.034
0.004034
-0.209
6
5.003
0.005003
7
6.024
0.006024
8
7.004
9
0.595
RPM
Velocity at Velocity at Total Head Power Out Suction Discharge (m) (KW) (m/s) (m/s) 0
Efficiency
5.95
0.684
1500
0
0
7.94
0.59
5.9
0.666
1500
0.1274722
0.1274722
7.93
0.08036048 12.066138
0.583
5.83
0.75
1500
0.2476638
0.2476638
7.87
0.15494983 20.6599777
0.58
5.8
0.822
1500
0.3772338
0.3772338
7.87
0.23601477 28.7122589
-2.09
0.578
5.78
0.864
1500
0.4977956
0.4977956
7.87
0.31144376 36.0467315
-0.211
-2.11
0.573
5.73
0.924
1500
0.6173702
0.6173702
7 .8 4
0 .3 84 78 27 4 1 .6 43 15 3
-0.213
-2.13
0.566
5.66
0.96
1500
0.7433616
0.7433616
7.79
0.46035348 47.9534873
0.007004
-0.215
-2.15
0.556
5.56
0.978
1500
0.8642936
0.8642936
7.71
0.52974824 54.1664867
8.035
0.008035
-0.216
-2.16
0.541
5.41
1.02
1500
0.991519
0.991519
7.57
0.59669276 58.4992901
10
8.524
0.008524
-0.218
-2.18
0.535
5.35
1.03
1500
1.0518616
1.0518616
7.53
0.62966191 61.1322246
11
9.01
0.00901
-0.22
-2.2
0.52
5.2
1.05
1500
1.111834
1.111834
7.4
0.65407194 62.2925657
12
9.506
0.009506
-0.221
-2.21
0.507
5.07
1.08
1500
1.1730404
1.1730404
7.28
0.6788881 62.8600093
13
10.065
0.010065
-0.224
-2.24
0.487
4.87
1.09
1500
1.242021
1.242021
7.11
0.70202469 64.405935
14
10.504
0.010504
-0.225
-2.25
0.465
4.65
1.1
1500
1.2961936
1.2961936
6.9
0.71100526 64.6368415
15
11.025
0.011025
-0.228
-2.28
0.447
4.47
1.11
1500
1.360485
1.360485
6.75
0.73004794 65.7700845
16
11.508
0.011508
-0.23
-2.3
0.428
4.28
1.12
1500
1.4200872
1.4200872
6.58
0.7428391 66.3249195
17
12.005
0.012005
-0.232
-2.32
0.408
4.08
1.13
1500
1.481417
1.481417
6 .4
0 .7 53 72 19 6 6. 70 10 55
18
13.004
0.013004
-0.235
-2.35
0.348
3.48
1.17
1500
1.6046936
1.6046936
5.83
0.74372867 63.5665529
19
14.017
0.014017
-0.24
-2.4
0.285
2.85
1.18
1500
1.7296978
1.7296978
5.25
0.72191054 61.1788595
20
14.668
0.014668
-0.243
-2.43
0.227
2.27
1.19
1500
1.8100312
1.8100312
4.7
0.67629748 56.8317207
Fig. 5.11 Reading for 1500 rpm set
M.TECH DISSERTATION (TURBOMACHINE)
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0
APPENDIX – D SR.NO.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
FLOW (lps)
Flow (m3/s)
0 1.012 2.047 3.032 4.034 5.016 6.026 7.046 8.034 9.003 10.035 11.0007 12.012 13.001 14.018 15.06 16.056 17.023 18.03 19.036
0 0.001012 0.002047 0.003032 0.004034 0.005016 0.006026 0.007046 0.008034 0.009003 0.010035 0.0110007 0.012012 0.013001 0. 014018 0.01506 0.016056 0.017023 0.01803 0.019036
P suction (Kg/Cm2)
-0.194 -0.201 -0.213 -0.22 -0.227 -0.233 -0.236 -0.238 -0.24 -0.243 -0.245 -0.248 -0.251 -0.254 -0.257 -0.261 -0.264 -0.267 -0.271 -0.273
P suction (m of water)
-1.94 -2.01 -2.13 -2.2 -2.27 -2.33 -2.36 -2.38 -2.4 -2.43 -2.45 -2.48 -2.51 -2.54 -2.57 -2.61 -2.64 -2.67 -2.71 -2.73
P P discharge Power In Discharge (m of (KW) (Kg/Cm2) water)
1.431 1.441 1.45 1.458 1.458 1.455 1.449 1.441 1.429 1.419 1.404 1.386 1.362 1.326 1.286 1.227 1.176 1.118 1.055 0.964
14.31 14.41 14.5 14.58 14.58 14.55 14.49 14.41 14.29 14.19 14.04 13.86 13.62 13.26 12.86 12.27 11.76 11.18 10.55 9.64
1.58 1.67 1.81 1.91 2.05 2.17 2.32 2.4 2.52 2.61 2.75 2.82 2.97 3.13 3.34 3.39 3.47 3.55 3.6 3.69
RPM
Velocity at Velocity at Total Head Power Out Suction Discharge Efficiency (m) (KW) (m/s) (m/s)
2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200 2200
0 0 0.1248808 0.1248808 0.2525998 0.2525998 0.3741488 0.3741488 0.4977956 0.4977956 0.6189744 0.6189744 0.7436084 0.7436084 0.8694764 0.8694764 0.9913956 0.9913956 1.1109702 1.1109702 1.238319 1.238319 1.3574864 1.35748638 1.4822808 1.4822808 1.6043234 1.6043234 1.7298212 1.7298212 1.858404 1 .858404 1.9813104 1.9813104 2.1006382 2.1006382 2.224902 2.224902 2.3490424 2.3490424
16.25 16.42 16.63 16.78 16.85 16.88 16.85 16.79 16.69 16.62 16.49 16.34 16.13 15.8 15.43 14.88 14.4 13.85 13.26 12.37
0 0.16301316 0.33394819 0.49910298 0.66681415 0.8306135 0.99608876 1.16054596 1.31539798 1.46786893 1.62333084 1.7633616 1.9007224 2.015129 2.12188083 2.19835037 2.26813478 2.31288948 2.34535322 2.31001289
Fig. 5.12Reading for 2200 rpm set
M.TECH DISSERTATION (TURBOMACHINE)
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0 9.76126721 18.4501765 26.1310459 32.5275195 38.2771191 42.9348604 48.3560815 52.1983326 56.2401888 59.0302124 62.5305534 63.997388 64.3811181 63.5293661 64.8480935 65.3641148 65.1518162 65.1487005 62.6019753
APPENDIX – E SR.NO.
FLOW (lps)
Flow (m3/s)
P suction (Kg/Cm2)
P suction (m of water)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 1.521 3.029 4.504 6.047 7.518 9.02 10.518 12.076 13.533 15.034 16.507 18.019 19.515 21.047 22.502 24.036 25.519 27.005 28.506
0 0.001521 0.003029 0.004504 0.006047 0.007518 0.00902 0.010518 0.012076 0.013533 0.015034 0.016507 0.018019 0.019515 0.021047 0.022502 0.024036 0.025519 0.027005 0.028506
-0.171 -0.184 -0.192 -0.22 -0.23 -0.245 -0.25 -0.251 -0.254 -0.256 -0.261 -0.266 -0.271 -0.276 -0.284 -0.292 -0.295 -0.31 -0.329 -0.34
-1.71 -1.84 -1.92 -2.2 -2.3 -2.45 -2.5 -2.51 -2.54 -2.56 -2.61 -2.66 -2.71 -2.76 -2.84 -2.92 -2.95 -3.1 -3.29 -3.4
P P discharge Power In Discharge (m of (KW) (Kg/Cm2) water)
2.737 2.724 2.723 2.722 2.72 2.71 2.7 2.69 2.66 2.602 2.561 2.47 2.39 2.286 2.15 2.01 1.85 1.7 1.502 1.308
27.37 27.24 27.23 27.22 27.2 27.1 27 26.9 26.6 26.02 25.61 24.7 23.9 22.86 21.5 20.1 18.5 17 15.02 13.08
3.46 3.61 3.97 4.39 4.69 5.09 5.31 5.68 5.96 6.19 6.43 6.65 6.88 7.12 7.31 7.45 7.62 7.74 7.88 7.93
RPM
Velocity at Velocity at Total Head Power Out Suction Discharge Efficiency (m) (KW) (m/s) (m/s)
2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900 2900
0 0 0.1876914 0.1876914 0.3737786 0.3737786 0.5557936 0.5557936 0.7461998 0.7461998 0.9277212 0.9277212 1.113068 1.113068 1.2979212 1.2979212 1.4901784 1.4901784 1.6699722 1.6699722 1.8551956 1.8551956 2.0369638 2.0369638 2.2235446 2.2235446 2.408151 2.408151 2.5971998 2.5971998 2.7767468 2.7767468 2.9660424 2.9660424 3.1490446 3.1490446 3.332417 3.332417 3.5176404 3.5176404
29.08 29.08 29.15 29.42 29.5 29.55 29.5 29.41 29.14 28.58 28.22 27.36 26.61 25.62 24.34 23.02 21.45 20.1 18.31 16.48
0 0.43390297 0.86617738 1.29990034 1.74997157 2.1793592 2.6103429 3.03457027 3.45208642 3.7942445 4.1619855 4.4305052 4.7037536 4.90474788 5.02550584 5.08154115 5.05776328 5.03186194 4.85066781 4.6085308
Fig. 5.13 Reading for 2900 rpm set
M.TECH DISSERTATION (TURBOMACHINE)
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0 12.0194729 21.8180701 29.6104861 37.3128265 42.816487 49.159 53.4255329 57.9209131 61.2963571 64.7276127 66.624139 68.368512 68.8869085 68.74837 68.2086061 66.3748462 65.0111362 61.556698 58.115143
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Stepanoff, A. J. (1957). Centrifugal Pump (Vol. 2 nd Edition). John Wiley and Sons.
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M.TECH DISSERTATION (TURBOMACHINE)
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