Turbomachinery Design and Theory - sv.20file.org

1 2 Hydraulic INTRODUCTIONH ydraulics is defined as the science of the conveyance of liquids through pump is often used to raise water from a low level to a high level where it canbe stored in a tank. Most of the Theory applicable to hydraulic pumps has beenderived using water as the working fluid, but other liquids can also be used. In thischapter, we will assume that liquids are totally incompressible unless otherwisespecified. This means that the density of liquids will be considered constant nomatter how much pressure is applied. Unless the change in pressure in a particularsituation is very great, this assumption will not cause a significant error incalculations. Centrifugal and axial flow pumps are very common hydraulicpumps. Both work on the principle that the energy of the liquid is increased byimparting kinetic energy to it as it flows through the pump. This energy issupplied by the impeller, which is driven by an electric motor or some other centrifugal and axial flow pumps will be discussed separately in thefollowing CENTRIFUGAL PUMPSThe three important parts of centrifugal pumps are (1) the impeller, (2) the volutecasing, and (3) the 2003 by Marcel Dekker, Inc.

2 All Rights ImpellerThe centrifugal pump is used to raise liquids from a lower to a higher level bycreating the required pressure with the help of centrifugal action. Whirlingmotion is imparted to the liquid by means of backward curved blades mounted ona wheel known as the impeller. As the impeller rotates, the fluid that is drawn intothe blade passages at the impeller inlet or eye is accelerated as it is forced radiallyoutwards. In this way, the static pressure at the outer radius is much higher than atthe eye inlet radius. The water coming out of the impeller is then lead through thepump casing under high pressure. The fluid has a very high velocity at the outerradius of the impeller, and, to recover this kinetic energy by changing it intopressure energy, diffuser blades mounted on a diffuser ring may be used. Thestationary blade passages have an increasing cross-sectional area. As the fluidmoves through them, diffusion action takes place and hence the kinetic energy isconverted into pressure energy.

3 Vaneless diffuser passages may also be used. Thefluid moves from the diffuser blades into the volute casing. The functions of avolute casing can be summarized as follows: It collects water and conveys it tothe pump outlet. The shape of the casing is such that its area of cross-sectiongradually increases towards the outlet of the pump. As the flowing waterprogresses towards the delivery pipe, more and more water is added from theoutlet periphery of the impeller. Figure shows a centrifugal pump impellerwith the velocity triangles at inlet and the best efficiency of the pump, it is assumed that water enters theimpeller radially, ,a1 908andCw1 0. Using Euler s pump equation, thework done per second on the water per unit mass of fluid flowingE Wm U2Cw22U1Cw1 2:1 WhereCwis the component of absolute velocity in the tangential to as the Euler head and represents the ideal or theoretical headdeveloped by the impeller only.

4 The flow rate isQ 2pr1Cr1b1 2pr2Cr2b2 2:2 WhereCris the radial component of absolute velocity and is perpendicular to thetangent at the inlet and outlet andbis the width of the blade. For shockless entryand exit to the vanes, water enters and leaves the vane tips in a direction parallelto their relative velocities at the two discussed in Chapter 1, the work done on the water by the pump consistsof the following three parts:1. The part (C22 C12)/2 represents the change in kinetic energy of The part (U22 U12)/2 represents the effect of the centrifugal head orenergy produced by the 248 Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved3. The part (V222V12)/2 represents the change in static pressure of theliquid, if the losses in the impeller are SLIP FACTORFrom the preceding section, it may be seen that there is no assurance that theactual fluid will follow the blade shape and leave the impeller in a radialdirection.

5 There is usually a slight slippage of the fluid with respect to the bladerotation. Figure shows the velocity triangles at impeller Fig. ,b20is the angle at which the fluid leaves the impeller, andb2isthe actual blade angle, andCw2andCw20are the tangential components ofabsolute velocity corresponding to the anglesb2andb20, respectively. Thus,Cw2is reduced toCw20and the differenceDCwis defined as the slip. The slip factoris defined asSlip factor;s Cw20Cw2 According to Stodola s Theory , slip in centrifugal pumps and compressors is dueto relative rotation of fluid in a direction opposite to that of impeller with the sameFigure triangles for centrifugal pump Pumps49 Copyright 2003 by Marcel Dekker, Inc. All Rights Reservedangular velocity as that of an impeller. Figure shows the leading side of ablade, where there is a high-pressure region while on the trailing side of the bladethere is a low-pressure to the lower pressure on the trailing face, there will be a higher velocityand a velocity gradient across the passage.

6 This pressure distribution is associatedwith the existence of circulation around the blade, so that low velocity on the high-pressure side and high velocity on the low-pressure side and velocity distributionis not uniform at any radius. Due to this fact, the flow may separate from thesuction surface of the blade. Thus,Cw2is less thanCw20and the difference isdefined as the slip. Another way of looking at this effect, as given by Stodola, isshown in Fig. , the impeller itself has an angular velocityvso that, relative tothe impeller, the fluid must have an angular velocity of2v; the result of this beinga circulatory motion relative to the channel or relative eddy. The net result of theprevious discussion is that the fluid is discharged from the impeller at an anglerelative to the impeller, which is less than the vane angle as mentioned triangle at impeller outlet with distribution on impeller vane. LP low pressure, HP 250 Copyright 2003 by Marcel Dekker, Inc.

7 All Rights ReservedHence, the slip factorsis defined ass C0w2Cw2 2:3 For purely radial blades, which are often used in centrifugal compressors,b2willbe 908and the Stodola slip factor becomess 12pn 2:4 wherenis the number of vanes. The Stanitz slip factor is given bys 120:63pn 2:5 When applying a slip factor, the Euler pump equation becomesWm sU2Cw22U1Cw1 2:6 Typically, the slip factor lies in the region of , while the slip occurs even if thefluid is PUMP LOSSESThe following are the various losses occurring during the operation of acentrifugal Eddy losses at entrance and exit of impeller, friction losses in theimpeller, frictional and eddy losses in the diffuser, if Losses in the suction and delivery pipe. The above losses are known ashydraulic Mechanical losses are losses due to friction of the main bearings, andstuffing boxes. Thus, the energy supplied by the prime mover toFigure eddy in impeller Pumps51 Copyright 2003 by Marcel Dekker, Inc.

8 All Rights Reservedimpeller is equal to the energy produced by impeller plus mechanicallosses. A number of efficiencies are associated with these the density of liquid;Q, flow rate;H, total head developed by thepump;Ps, shaft power input;Hi, total head across the impeller; andhi, head lossin the impeller. Then, the overall efficiencyhois given by:ho Fluid power developed by pumpShaft power input rgQHPs 2:7 Casing efficiencyhcis given by:hc Fluid power at casing outlet/fluid power at casing inlet Fluid power at casing outlet/ fluid power developed byimpeller2leakage loss rgQH/rgQHi H/Hi 2:8 Impeller efficiencyhiis given by:hi Fluid power at impeller exit/fluidpower supplied to impeller Fluid power at impeller exit/ fluid powerdeveloped by impeller impeller loss rgQiHi/rgQiHi hi Hi/ Hi hi 2:9 Volumetric efficiencyhvis given by:hv Flow rate through pump/flow rate through impeller Q/ Q q 2:10 Mechanical efficiencyhmis given by:hm Fluid power supplied to the impeller/powerinput to the shaft rgQi hi Hi /Ps 2:11 Therefore,ho hchihvhm 2:12 Chapter 252 Copyright 2003 by Marcel Dekker, Inc.

9 All Rights ReservedA hydraulic efficiency may be defined ashh Actual head developed by pumpTheoretical head developed by impeller H Hi hi 2:13 The headHis also known as manometric THE EFFECT OF IMPELLER BLADE SHAPEON PERFORMANCEThe various blade shapes utilized in impellers of centrifugal pumps/compressorsare shown in Fig. The blade shapes can be classified as:1. Backward-curved blades (b2,908)2. Radial blades (b2 908)3. Forward-curved blades ( )As shown in Fig. , for backward-curved vanes, the value ofCw2(whirlcomponent at outlet) is much reduced, and thus, such rotors have a low energytransfer for a given impeller tip speed, while forward-curved vanes have a highvalue of energy transfer. Therefore, it is desirable to Design for high values ofb2(over 908), but the velocity diagrams show that this also leads to a very high valueofC2. High kinetic energy is seldom required, and its reduction to static pressureby diffusion in a fixed casing is difficult to perform in a reasonable sized , radial vanes (b2 908) have some particular advantages for very high-speed compressors where the highest possible pressure is required.

10 Radial vanesare relatively easy to manufacture and introduce no complex bending stresses(Fig. ).Figure pump outlet velocity triangles for varying blade outlet Pumps53 Copyright 2003 by Marcel Dekker, Inc. All Rights VOLUTE OR SCROLL COLLECTORA volute or scroll collector consists of a circular passage of increasing cross-sectional area (Fig. ). The advantage of volute is its simplicity and low cross-sectional area increases as the increment of discharge increasesaround the periphery of the impeller, and, if the velocity is constant in the volute,Figure for varying outlet blade or scroll 254 Copyright 2003 by Marcel Dekker, Inc. All Rights Reservedthen the static pressure is likewise constant and the radial thrust will be zero. Anydeviation in capacity ( , flow rate) from the Design condition will result in aradial thrust which if allowed to persist could result in shaft cross-sectional shape of the volute is generally similar to that shown inFig.