GRUNDFOS RESEARCH AND TECHNOLOGY The Centrifugal Pump
The Centrifugal Pump 5
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Preface In the Department of Structural and Fluid Mechanics we are happy to present the first English edition of the book: ’The Centrifugal Pump’. We have written the book because we want to share our knowledge of pump hydraulics, pump design and the basic pump terms which we use in our daily work. ’The Centrifugal Pump’ is primarily meant as an internal book and is aimed at technicians who work with development and construction of pump components.
Contents Chapter 1. Introduction to Centrifugal Pumps................11 1.1 1.2 Principle of centrifugal pumps. ......................................12 The pump’s hydraulic components.............................13 1.2.1 Inlet flange and inlet.............................................14 1.2.2 Impeller..........................................................................15 1.2.3 Coupling and drive.................................................17 1.2.4 Impeller seal.................................
4.4 4.5 4.6 4.7 4.8 4.9 Usage of Euler’s pump equation. ................................... 67 Affinity rules................................................................................ 68 4.5.1 Derivation of affinity rules............................... 70 Pre-rotation..................................................................................72 Slip......................................................................................................73 The pump’s specific speed..................
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Chapter 1 Introduction to centrifugal pumps 1.1 Principle of the centrifugal pump 1.2 Hydraulic components 1.3 Pump types and systems 1.
1. Introduction to Centrifugal Pumps 1. Introduction to Centrifugal Pumps In this chapter, we introduce the components in the centrifugal pump and a range of the pump types produced by Grundfos. This chapter provides the reader with a basic understanding of the principles of the centrifugal pump and pump terminology. The centrifugal pump is the most used pump type in the world.
1.2 Hydraulic components The principles of the hydraulic components are common for most centrifugal pumps. The hydraulic components are the parts in contact with the fluid. Figure 1.2 shows the hydraulic components in a single-stage inline pump. The subsequent sections describe the components from the inlet flange to the outlet flange. Figure 1.2: Hydraulic components.
1. Introduction to Centrifugal Pumps 1.2.1 Inlet flange and inlet The pump is connected to the piping system through its inlet and outlet flanges. The design of the flanges depends on the pump application. Some pump types have no inlet flange because the inlet is not mounted on a pipe but submerged directly in the fluid. The inlet guides the fluid to the impeller eye. The design of the inlet depends on the pump type.
The design of the inlet aims at creating a uniform velocity profile into the impeller since this leads to the best performance. Figure 1.4 shows an example of the velocity distribution at different cross-sections in the inlet. 1.2.2 Impeller The blades of the rotating impeller transfer energy to the fluid there by increasing pressure and velocity. The fluid is sucked into the impeller at the impeller eye and flows through the impeller channels formed by the blades between the shroud and hub, see figure 1.
1. Introduction to Centrifugal Pumps The impeller’s ability to increase pressure and create flow depends mainly on whether the fluid runs radially or axially through the impeller, see figure 1.6. In a radial impeller, there is a significant difference between the inlet diameter and the outlet diameter and also between the outlet diameter and the outlet width, which is the channel height at the impeller exit. In this construction, the centrifugal forces result in high pressure and low flow.
1.2.3 Coupling and drive The impeller is usually driven by an electric motor. The coupling between motor and hydraulics is a weak point because it is difficult to seal a rotating shaft. In connection with the coupling, distinction is made between two types of pumps: Dry-runner pumps and canned rotor type pump. The advantage of the dry-runner pump compared to the canned rotor type pump is the use of standardized motors. The disadvantage is the sealing between the motor and impeller.
1. Introduction to Centrifugal Pumps In pumps with a magnetic drive, the motor and the fluid are separated by a non-magnetizable rotor can which eliminates the problem of sealing a rotating shaft. On this type of pump, the impeller shaft has a line of fixed magnets called the inner magnets. The motor shaft ends in a cup where the outer magnets are mounted on the inside of the cup, see figure 1.11. The rotor can is fixed in the pump housing between the impeller shaft and the cup.
Achieving an optimal balance between leakage and friction is an essential goal when designing an impeller seal. A small gap limits the leak flow but increases the friction and risk of drag and noise. A small gap also increases requirements to machining precision and assembling resulting in higher production costs. To achieve optimal balance between leakage and friction, the pump type and size must be taken into consideration. 1.2.
1. Introduction to Centrifugal Pumps The axial bearing absorbs the entire axial thrust and is therefore exposed to the forces affecting the impeller. Outlet pressure Atmospheric pressure Outlet pressure The impeller must be axially balanced if it is not possible to absorb the entire axial thrust in the axial bearing. There are several possibilities of reducing the thrust on the shaft and thereby balance the axial bearing. All axial balancing methods result in hydraulic losses.
A fourth method to balance the axial thrust is to mount fins on the pump housing in the cavity below the impeller, see figure 1.19. In this case, the primary flow velocity in the cavity below the impeller is reduced whereby the pressure increases on the shroud. This type of axial balancing increases disc friction and leak loss because of the higher pressure. Blades Figure 1.18: Axial thrust reduction through blades on the back of the hub plate. 1.2.
1. Introduction to Centrifugal Pumps The volute casing consists of three main components: Ring diffusor, volute and outlet diffusor, see figure 1.21. An energy conversion between velocity and pressure occurs in each of the three components. The primary ring diffusor function is to guide the fluid from the impeller to the volute. The cross-section area in the ring diffussor is increased because of the increase in diameter from the impeller to the volute.
1.2.7 Return channel and outer sleeve To increase the pressure rise over the pump, more impellers can be connected in series. The return channel leads the fluid from one impeller to the next, see figure 1.22. An impeller and a return channel are either called a stage or a chamber. The chambers in a multistage pump are altogether called the chamber stack.
1. Introduction to Centrifugal Pumps 1.3 Pump types and systems This section describes a selection of the centrifugal pumps produced by Grundfos. The pumps are divided in five overall groups: Circulation pumps, pumps for pressure boosting and fluid transport, water supply pumps, industrial pumps and wastewater pumps. Many of the pump types can be used in different applications. Circulation pumps are primarily used for circulation of water in closed systems e.g.
1.3.1. The UP pump Circulation pumps are used for heating, circulation of cold water, ventilation and aircondition systems in houses, office buildings, hotels, etc. Some of the pumps are installed in heating systems at the end user. Others are sold to OEM customers (Original Equipment Manufacturer) that integrate the pumps into gas furnace systems. It is an inline pump with a canned rotor which only has static sealings. The pump is designed to minimise pipetransferred noise.
1. Introduction to Centrifugal Pumps 1.3.5 The SP pump The SP pump is a multi-stage submersible pump which is used for raw water supply, ground water lowering and pressure boosting. The SP pump can also be used for pumping corrosive fluids such as sea water. The motor is mounted under the chamber stack, and the inlet to the pump is placed between motor and chamber stack. The pump diameter is designed to the size of a standard borehole.
1.3.8 The SE pump The SE pump is used for pumping wastewater, water containing sludge and solids. The pump is unique in the wastewater market because it can be installed submerged in a waste water pit as well as installed dry in a pipe system. The series of SE pumps contains both vortex pumps and single-channel pumps. The single-channel pumps are characterised by a large free passage, and the pump specification states the maximum diameter for solids passing through the pump. 1.3.
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Chapter 2 Performance curves 2.1 Standard curves 2.2 Pressure H [m] 2.3 Absolute and relative pressure 50 2.4 Head 40 2.5 Differential pressure across the pump - description of differential pressure 2.6 Energy equation for an ideal flow 2.7 Power 2.8 Hydraulic power 2.9 EfficiencyHead 2.10 NPSH, Net Positive Suction Head 30 2.11 Axial thrust Efficiency 20 2.12 Radial thrust 10 2.
2. Performance curves 2. Performance curves The pump performance is normally described by a set of curves. This chapter explains how these curves are interpretated and the basis for the curves. 2.1 Standard curves Performance curves are used by the customer to select pump matching his requirements for a given application. The data sheet contains information about the head (H) at different flows (Q), see figure 2.1. The requirements for head and flow determine the overall dimensions of the pump.
In addition to head, the power consumption (P) is also to be found in the data sheet. The power consumption is used for dimensioning of the installations which must supply the pump with energy. The power consumption is like the head shown as a function of the flow. Information about the pump efficiency (η) and NPSH can also be found in the data sheet. NPSH is an abbreviation for ’Net Positive Suction Head’.
2. Performance curves 2.2 Pressure Pressure (p) is an expression of force per unit area and is split into static and dynamic pressure. The sum of the two pressures is the total pressure: p tot = pstat + pdyn [Pa] where 1 ⋅ ρ ⋅ V[Pa] 2 ptot = Total [Pa] pdyn =pressure 2 pstat = Static pressure [Pa] pdyn = Dynamic ∆p tot = ∆pressure pstat + ∆p[Pa] dyn + ∆p geo (2.1) (2.2) [Pa] (2.5) ∆pstat = ispstat, (2.
p tot = pstat + pdyn [Pa] (2.1) 2.3 Absolute and relative pressure 1 ⋅ρ⋅V Pressure in2 two or relative [Pa]different ways: absolute pressure (2.2) pdynis =defined 2 pressure. Absolute pressure refers to the absolute zero, and absolute pressure thus only a positive [Pa] Relative pressure refers ∆pcan ∆pstat + be ∆pdyn + ∆pgeo number. (2.5) to the tot = pressure of the surroundings. A positive relative pressure means that the ∆pisstatabove (2.
p tot = pstat + pdyn [Pa] (2.1) 2. Performance curves pdyn = 1 ⋅ ρ ⋅ V 2 [Pa] 2 (2.2) ∆p tot = ∆pstat + ∆pdyn + ∆pgeo [Pa] 2.4 Head (2.5) The different performance curves are introduced on the following pages. ∆pstat = pstat, out − pstat, in [Pa] (2.6) Δp tot H= ρ⋅ g [m] (2.4) 34 30 20 10 0 0 [m] [m] or 10 20 30 40 50 60 70 Q [m3/h] Figure 2.5: A typical QH curve for a centrifugal pump; a small flow gives a high head and a large flow gives a low head.
2.5 Differential pressure across the pump - description of differential pressure (2.1) p tot = pstat + pdyn [Pa] 2.5.1 Total pressure difference The total pressure difference across the pump is calculated on the basis of three contributions: (2.2) pdyn = 1 ⋅ ρ ⋅ V 2 [Pa] 2 ∆p tot = ∆pstat + ∆pdyn + ∆pgeo [Pa] (2.5) where ∆pstat = pstat, out − pstat, in [Pa] (2.6) Δptot = Total pressure difference across the pump [Pa] 2 2 1 ⋅ ρ ⋅ V difference 1 ⋅ ρ ⋅ Vacross Δpstat = ∆Static the [Pa ] pump [Pa] (2.
2 [Pa] pdyn = 1 ⋅ ρ ⋅ Vcurves 2. Performance 2 ∆p = ∆pstatpdyn + ∆p[Pa p dyn]+ ∆p geo tottot= pstat + (2.2) [Pa] (2.5) (2.1) In practise, the dynamic pressure and the flow velocity before and after the ∆pstat = pstat, out − pstat, in [Pa] (2.6) pump are not measured during test of pumps. Instead, the dynamic pressure difference and pipe diameter of the(2.2) inlet and pdyncan = 1be ⋅ ρcalculated ⋅ V 2 2 [Pa]1if the flow 2 1 2 [ ] (2.
∆pdyn = 1 ⋅ ρ ⋅ Vout 2 − 1 ⋅ ρ ⋅ Vin2 2 2 [Pa] (2.7) 2 Q 1 1 ⋅ Δpdyn = 1 ⋅ ρ ⋅ (2.8) D 4 − D 4 [Pa] 2 π 2.6 Energy equation for an ideal flow out in 4 The energy equation for an ideal flow describes that the sum of pressure energy, velocity energy and potential energy is constant. Named after the Swiss physicist Daniel Bernoulli, the equation is known as Bernoulli’s (2.
2. Performance curves 2.7 Power The power curves show the flow, see p tot = pstat + pdyn [Pa]energy transfer rate as a function of(2.1) figure 2.7. The power is given in Watt [W]. Distinction is made between three kinds of power, see figure 2.8: • Supplied power from external electricity source to the motor and (2.2) pdyn = 1 ⋅ ρ ⋅ V 2 [Pa] 2 controller (P1) • Shaft power transferred from the motor to the shaft (P2) ∆p tot = ∆pstat + ∆pdyn + ∆pgeo [Pa] (2.
⋅ ∆p geo geo = ∆z ⋅ ρ g [Pa 2] Q 1 1 ⋅ − Δpdyn =22 1 ⋅ ρ ⋅ Dout4 m 22Din 4 p + V +2 g ⋅ z =πConstant 4 s 22 ρ 2 (2.9) (2.9) [Pa] (2.8) (2.10) 2.9 Efficiency [Pa] pabs = prel + pbar (2.3) (2.3) rel The totalabsefficiency (ηbartot) is the ratio between hydraulic power and supplied [Paefficiency ] p geo =2.9 ∆z shows ⋅ ρ ⋅ g the power. ∆Figure curves for the pump (ηhyd(2.9) ) and for a Δp tot tot (2.4) (2.
2 2 2 Q 2. Performance curves ⋅ Δp = 1 ⋅ ρ ⋅ 2 dyn π 4 1 1 D 4 − D 4 in out [Pa] (2.8) 2.10 NPSH, Net Positive Suction Head NPSH is a term describing conditions related to cavitation, which is undesired and= harmful. (2.9) ∆p geo ∆z ⋅ ρ ⋅ g [Pa] 2 2 Cavitation creation of vapourm bubbles in areas where the pressure p isVthe g z Constant + + ⋅ = (2.10) locally drops The extent of cavitation depends 2 ρ 2to the fluid vapour pressure.
ρ + 2 + g ⋅ z = Constant pabs = prel + pbar (2.10) s2 [Pa] (2.3) Δp tot (2.4) [m] H= g NPSH Required and is an expression of the lowest NPSH NPSHR standsρ ⋅for value required operating conditions. The absolute pressure (2.11) Phyd = H for ⋅ g acceptable ⋅ ρ ⋅ Q = ∆p tot ⋅ Q [W ] pabs,tot,in can be calculated from a given value of NPSHR and the fluid vapour Phyd pressure by inserting NPSH in the formula (2.16) instead of NPSHA. (2.
pabs = prel + pbar Δp tot [Pa] ] ∆pPerformance Pa]curves H ∆=z ⋅ ρ ⋅ g [[m geo = 2. ρ⋅ g (2.3) (2.9) (2.4) 2 2 p VP ⋅ ρ ⋅ Q = ∆pmtot ⋅ Q [W] hyd + + g= ⋅Hz ⋅=gConstant (2.10) (2.11) 2 ρ 2 2.1 Pump drawing from s a well Example Phyd [⋅]100 % ] η hyd +=p pabs = p (2.3) (2.12) bar P2 [Pa A pump rel must draw water from a reservoir where the water level is 3 meters below the pump. To calculate the NPSHA value, it is necessary to know the P Δp tot (2.4) (2.
tot (2.4) [m] H= Δp tot ρ ⋅ g (2.4) [m] H= ρ⋅ g (2.11) Phyd = H ⋅ g ⋅ ρ ⋅ Q = ∆p tot ⋅ Q [W] (2.11) Phyd = H ⋅ g ⋅ ρ ⋅ Q = ∆p tot ⋅ Q [W] Phyd (2.12) [⋅ 100 % ] η hyd = Phyd 2 Example in (2.12) [⋅ P100 %a] closed system η hyd = 2.2 Pump P2 Phyd System [there ] free water surface to refer to. This ⋅ 100 is % no (2.13) = η tot system, In a closed example Phyd P1 [⋅ 100 % ] sensor’s placement above the reference (2.13) η tot = how the pstat, in shows pressure plane can P1 be usedPto find the absolute 2.13. (2.
2. Performance curves 2.11 Axial thrust Axial thrust is the sum of forces acting on the shaft in axial direction, see figure 2.14. Axial thrust is mainly caused by forces from the pressure difference between the impeller’s hub plate and shroud plate, see section 1.2.5. The size and direction of the axial thrust can be used to specify the size of the bearings and the design of the motor. Pumps with up-thrust require locked bearings.
2.13 Summary Chapter 2 explains the terms used to describe a pump’s performance and shows curves for head, power, efficiency, NPSH and thrust impacts. Furthermore, the two terms head and NPSH are clarified with calculation examples.
Chapter 3 Pumps operating in systems Tank on roof 3.1 Single pump in a system 3.2 Pumps operated in parallel 3.3 Pumps operating in series 3.4 Regulation of pumps 3.5 Annual energy consumption 3.6 Energy efficiency index (EEI) 3.
3. Pumps operating in systems 3. Pumps operating in systems This chapter explains how pumps operate in a system and how they can be regulated. The chapter also explains the energy index for small circulation pumps. A pump is always connected to a system where it must circulate or lift fluid. The energy added to the fluid by the pump is partly lost as friction in the pipe system or used to increase the head. Implementing a pump into a system results in a common operating point.
3.1 Single pump in a system A system characteristic is described by a parabola due to an increase in friction loss related to the flow squared. The system characteristic is described by a steep parabola if the resistance in the system is high. The parabola flattens when the resistance decreases. Changing the settings of the valves in the system changes the characteristics. The operating point is found where the curve of the pump and the system characteristic intersect. In closed systems, see figure 3.
3. Pumps operating in systems 3.2 Pumps operated in parallel In systems with large variations in flow and a request for constant pressure, two or more pumps can be connected in parallel. This is often seen in larger supply systems or larger circulation systems such as central heating systems or district heating installations. H Hmax Hoperation, a= Hoperation, b Parallel-connected pumps are also used when regulation is required or if an auxiliary pump or standby pump is needed.
3.3 Pumps operated in series Centrifugal pumps are rarely connected in serial, but a multi-stage pump can be considered as a serial connection of single-stage pumps. However, single stages in multistage pumps can not be uncoupled. If one of the pumps in a serial connection is not operating, it causes a considerable resistance to the system. To avoid this, a bypass with a non-return valve could be build-in, see figure 3.6.
3. Pumps operating in systems 3.4.1 Throttle regulation Installing a throttle valve in serial with the pump it can change the system characteristic, see figure 3.7. The resistance in the entire system can be regulated by changing the valve settings and thereby adjusting the flow as needed. A lower power consumption can sometimes be achieved by installing a throttle valve. However, it depends on the power curve and thus the specific speed of the pump.
3.4.3 Start/stop regulation In systems with varying pump requirements, it can be an advantage to use a number of smaller parallel-connected pumps instead of one larger pump. The pumps can then be started and stopped depending on the load and a better adjustment to the requirements can be achieved. 3.4.4 Speed control When the pump speed is regulated, the QH, power and NPSH curves are changed. The conversion in speed is made by means of the affinity equations. These are futher described in section 4.
3. Pumps operating in systems Proportional-pressure control Proportional-pressure control strives to keep the pump head proportional to the flow. This is done by changing the speed in relation to the current flow. Regulation can be performed up to a maximum speed, from that point the curve will follow this speed. The proportional curve is an approximative system characteristic as described in section 3.1 where the needed flow and head can be delivered at varying needs.
H H Q Q P2 P2 Q Q η η Q Q n n Q Figure 3.12: Example of proportional-pressure control. 55 Q Figure 3.13: Example of constant-pressure control.
3. Pumps operating in systems 3.5. Annual energy consumption Like energy labelling of refrigerators and freezers, a corresponding labelling for pumps exists. This energy label applies for small circulation pumps and makes it easy for consumers to choose a pump which minimises the power consumption. The power consumption of a single pump is small but because the worldwide number of installed pumps is very large, the accumulated energy consumption is big.
nB (3.1) nA 3.6 Energy efficiency index (EEI) 2 In 2003 a study of anmajor part of the circulation pumps on the market was B ⋅ H H = (3.2) B TheA purpose conducted. n was to create a frame of reference for a representa A tive power consumption for a specific pump. The result is the curve shown 3 in figure 3.16. Based n on the study the magnitude of a representative power (3.3) PB = PA ⋅ B consumption of an pump at a given Phyd,max can be read from the A n average curve. 2 n (3.
3. Pumps operating in systems 3.7 Summary In chapter 3 we have studied the correlation between pump and system from a single circulation pump to water supply systems with several parallel coupled multi-stage pumps. We have described the most common regulation methods from an energy efficient view point and introduced the energy index term.
Chapter 4 Pump theory 4.1 Velocity triangles 4.2 Euler’s pump equation 4.3 Blade form and pump curve C2 4.4 Usage of Euler’s pump equation 4.5 Affinity rules C2m U2 C2u 4.6 Inlet rotation β2 4.7 Slip 2 W1 4.8 Specific speed of a pump 4.
4. Pump theory 4. Pump theory The purpose of this chapter is to describe the theoretical foundation of energy conversion in a centrifugal pump. Despite advanced calculation methods which have seen the light of day in the last couple of years, there is still much to be learned by evaluating the pump’s performance based on fundamental and simple models. When the pump operates, energy is added to the shaft in the form of mechanical energy.
C2 Figure 4.2a: Velocity triangles positioned at the impeller inlet and outlet. W2 C2m U2 U2 β2 2 C1m α1 1 W2 C2 C2U C2m β2 U2 W1 β1 C2 C2m β2 W2 α2 C2U 2 α2 α2 C2U 1 W1 U1 ω Wβ1 1 r1 r2 U1 β1 α1 α1 C1m C1m Figure 4.2b: Velocity triangles U1 The second plane is defined by the meridional velocity and the tangential velocity. An example of velocity triangles is shown in figure 4.2.
4. Pump theory 4.1.1 Inlet Usually it is assumed that the flow at the impeller inlet is non-rotational. This means that α1=90°. The triangle is drawn as shown in figure 4.2 position 1, and C1m is calculated from the flow and the ring area in the inlet. The ring area can be calculated in different ways depending on impeller type (radial impeller or semi-axial impeller), see figure 4.3. For a radial impeller this is: A1 = 2 π ⋅ r1 ⋅ b1 [m2] (4.1) where r1 , hub + r1 , shroud ⋅ b1 inlet (4.
63 r1 , hub + r1 , shroud ⋅ b1 (4.2) [m2] (4.1) A1 = 2 π⋅ π⋅ r⋅1 ⋅ b1 [m2] 2 + r21 , shroud A1 = = 2 πQ⋅impeller r1 ⋅ br11, hub[m (4.1) ⋅ b1 (4.2) [m2] A 1 =2 ⋅ π ⋅ [ms2]] C (4.3) 1m A1 r r + 1 , hub 1 , shroud ⋅m (4.2) [m2] A = 2 Q⋅ πimpeller b1 ⋅ n m [ C111 m= = (4.3) 2] U 2 r r ⋅ π ⋅ ⋅ = ⋅ ω (4.4) [ ] 2 s 1 1] s A = 2 π ⋅ r ⋅ b [ m (4.1) A1 1 60 1 1 4.1.2 Outlet Q Cimpeller m As withCthe inlet,1 mthe velocity triangle at the outlet is drawn as(4.
r1 , hub + r1 , shroud ⋅ b1 (4.2) [m2] A1 = 2 ⋅ π ⋅ 2 2 A1 = 2 π ⋅ r1 ⋅ b1 [m ] (4.1) Q impeller m 4. Pump C 1 m =theory (4.3) r1 , hub[+sr1], shroud ⋅ b1 (4.2) [m2] A1 = 2 ⋅ π A⋅ 1 22 A1 ==22⋅ππ⋅⋅rr1 ⋅⋅b1n = [mr ]⋅ ω [ms ] (4.1) U (4.4) 1 1 Q impeller 60 m1 4.2 Euler’s pump equation [ ] C 1m = (4.3) r1 , shroud r1 , hubis+sthe 2 equation in connection with CA 1 Euler’s tan pump equation most important 1⋅ m (4.2) [ ] m A 2 b π = ⋅ ⋅ [ 2] (4.
ω− (rr2⋅ CC2U) − r1[Nm C1U]) T =P m= ⋅ (r m (4.12) m] Un 1[W] 1U (4.13) T⋅rC⋅ 2⋅ω [ ⋅=π 2⋅m ⋅ ω U2 =2 2 = r (4.9) s. 2 . (ω. r = 2 . . 60 2 C2U − ω r1 C1U ) . . . . = m ω (r2 C2U − r1 C1U ) = m . ( U2 . C2U − U1 . C1U ) . C − ω . r1 . C1U ) C m (4.13) P2 = T ⋅ .ω( ω . r[2W . ]2U . W 2 = = 2 mQ . ρ . ([Um (4.10) 2 ]C2U − U1 C1U ) s . . . . . = βm ( U C − U C ) sin ω 2(r2 2CU 2U − r11 C11UU ) 2 . (.ω Q.ρ ( U. .. C − U . . C. ) (4.14) Phyd = = ∆p totm⋅ C Q2 m r2[2W]22UU mω1 r1 1CU1U ) The head as: (4.
4. Pump theory When designing a pump, it is often assumed that there is no inlet rotation meaning that C1U equeals zero. H = U 2 ⋅ C 2U g [m] (4.20) ⋅ ⋅v [N] F =m 4.3 Blade shape and pump curve ⋅ ⋅ v = ρ ⋅ A ⋅ v 2 [N] ∆I = m β2 [N] β ∆I = F 1 β2 β1 (4.22) β2 β2 β1 2 2 U U2 − ⋅Q H= g π ⋅ D2 ⋅ b2 ⋅ g ⋅ tan( β2 ) �2�>90 o (4.21) �2�>90 o�2�>90 o β1 [m] β2 β1 β1 β2 = 90o β2 = 90βo2 = 90o U2 2 U 2 (4.23) (4.
4.4 Usage of Euler’s pump equation There is a close connection between the impeller geometry, Euler’s pump equation and the velocity triangles which can be used to predict the impact of changing the impeller geometry on the head. The individual part of Euler’s pump equation can be identified in the outlet velocity triangle, see figure 4.9. W2 C2m C2 α2 β2 Figure 4.
4. Pump theory In the following, the effect of reducing the outlet width b2 on the velocity triangles is discussed. From e.g. (4.6) and (4.8), the velocity C2m can be seen to be inversely proportional to b2. The size of C2m therefore increases when b2 decreases. U2 in equation (4.9) is seen to be independent of b2 and remains constant. The blade angle b2 does not change when changing b2. W2 C2 C2m β2 The velocity triangle can be plotted in the new situation, as shown in figure ⋅ C decrease and that 4.
Figure 4.12 shows an example of the changed head and power curves for a pump where the impeller diameter is machined to different radii in order to match different motor sizes at the same speed. The curves are shown based on formula (4.26). η [%] H [m] ø260 mm ø247 mm 20 ø234 mm ø221 mm 16 80 70 12 60 50 8 40 30 20 4 10 4 8 12 16 20 24 28 32 36 40 Q (m 3/h) P2 [kW] 3 2,5 2 1,5 1 0,5 69 Figure 4.12: Examples of curves for machined impellers at the same speed but different radii.
2,B =UQ2 A− ⋅ U2 B (4.21) ⋅ Q [m] HQ= n g πA⋅D2⋅ b2 ⋅ g ⋅ tan( β2 ) 2 nB Scaling of W C2 = ⋅ H H 2 A 4. PumpBtheory nA rotational speed C2m C2m,B 3 (4.22)β 2 nB PBB = Q PAA⋅ Q C2U,B C2U U nA 4.5.1 Derivation ofthe affinity rules 2 Scaling The affinity method preciseofwhen adjusting the speed up and down nisvery (4.23) ⋅ 2 ⋅bB HB = HA D rotational BnA B and when using geometrical scaling speed in all directions (3D scaling).
UB UB = U A= UA C m,B DA = C m,B C m,A = C m,A ⋅ bu,B C A C u,B Cu,A Cu,A (4.24) (4.24) UB n ⋅ D2,BCu,B CBm,B (4.24) (4.25) UB == nB ⋅ D=2,B (4.25) UA = n CAm,A ⋅ D2,ACu,A UA nA ⋅ D2,A Neglecting inlet rotation, the changes in flow, head and power consumption UB nB ⋅ D2,B (4.25) can be expressed as follows: = UA nA ⋅ D2,A Flow: Q = A 2 ⋅ C2m= π ⋅ D2 ⋅ b2 ⋅ C2m (4.26) Q = A 2 ⋅ C2m= π ⋅ D2 ⋅ b2 ⋅ C2m (4.
U1 4. Pump theory 4.6 Inlet rotation Inlet rotation means that the fluid is rotating before it enters the impeller. The fluid can rotate in two ways: either the same way as the impeller (co-rotation) or against the impeller (counter-rotation). Inlet rotation occurs as a consequence of a number of different factors, and a differentation between desired and undesired inlet rotation is made. In some cases inlet rotation can be used for correction of head and power consumption.
4.7 Slip In the derivation of Euler’s pump equation it is assumed that the flow follows the blade. In reality this is, however, not the case because the flow angle usually is smaller than the blade angle. This condition is called slip. Nevertheless, there is close connection between the flow angle and blade angle. An impeller has an endless number of blades which are extremely thin, then the flow lines will have the same shape as the blades.
Q A π ⋅ D2,A ⋅ b2,A C2m,A π ⋅D2,A⋅ b2,A⋅ nA⋅ D2,A D2,A b2,A nA 4. Pump theory H= U2,A ⋅ C 2U,A g (4.27) 2 2 4.8 Specific a pump HB speed U2,B ⋅of C2U,B ⋅ g U2,B ⋅ C2U,B nB⋅ D2,B ⋅ nB ⋅ D2,B D2,B nB = chapter 1, =pumps are =classified in many = As described ⋅ n ways for HA inU2,A ⋅ C2U,A ⋅ g U2,A ⋅ C2U,A nA⋅ D2,A⋅ nA ⋅ D2,A Ddifferent 2,A A example by usage or flange size.
Impeller shape nq Outlet velocity triangle 15 d1 0 d2 30 U2 d2/d1 = 2.0 - 1.5 50 W2 d1 C2 U2 C2U H 0 100 H % Hd Pd C2 C2U d2/d1 = 1.2 - 1.1 100 Pd H C2 W2 110 U2 W2 C2U C2 U2 C2U 100 P % 70 Pd 60 0 d2 155 Q/Qd 100 H % Hd U2 100 P % 80 Pd H 0 d1 165 Q/Qd 55 d2 90 110 P % 100 Pd Pd 100 d2/d1 = 1.5 - 1.3 W2 170 Q/Qd 70 C2U d2 d1 = d2 100 100 C2 % H H % Hd d1 100 Pd 80 C2U W2 130 P Pd 100 C2 U2 d2/d1 = 3.5 - 2.
Chapter 5 Pump losses 5.1 Loss types 5.2 Mechanical losses 5.3 Hydraulic losses 5.4 Loss distribution as function of specific speed 5.
5. Pump losses 5. Pump losses As described in chapter 4, Euler’s pump equation provides a simple, lossfree 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, see figures 5.1 and 5.2. The result is a reduction in efficiency.
Figure 5.3 shows the components in the pump which cause mechanical and hydraulic losses. It involves bearings, shaft seal, front and rear cavity seal, inlet, impeller and volute casing or return channel. Throughout the rest of the chapter this figure is used for illustrating where each type of loss occurs. Volute Diffuser Inner impeller surface Outer impeller surface Front cavity seal Inlet Bearings and shaft seal Figure 5.3: Loss causing components.
5. Pump losses 5.2 Mechanical losses The pump coupling or drive consists of bearings, shaft seals, gear, depending on pump type. These components all cause mechanical friction loss. The following deals with losses in the bearings and shaft seals. 5.2.1 Bearing loss and shaft seal loss Bearing and shaft seal losses - also called parasitic losses - are caused by friction. They are often modelled as a constant which is added to the power consumption.
5.3.1 Flow friction 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. Model Flow friction occurs in all the hydraulic components which the fluid flows through.
5. Pump losses Friction loss in pipes Pipe friction is the loss of energy which occurs in a pipe with flowing fluid. At the wall, the fluid velocity is zero whereas it attains a maximum value at the pipe center. Due to these velocity differences across the pipe, see figure 5.5, the fluid molecules rub against each other. This transforms kinetic energy to heat energy which can be considered as lost.
Equation (5.4) applies in general for all cross-sectional shapes. In cases where (5.1) to the = Ploss, = constant mechanical bearing + Ploss, shaft the pipePloss, has a circular cross-section, thesealhydraulic diameter is equal pipe diameter. The circular pipe is 2the cross-section type which has the smallest possible interior surface V compared to the cross-section(5.2) area and H loss, friktion = ζ ⋅ H dyn, in = ζ ⋅ 2g therefore the smallest flow resistance. LV 2 H loss, pipe = f (5.
5. Pump losses Turbulent flow is an unstable flow with strong mixing. Due to eddy motion most pipe flows are in practise turbulent. The friction coefficient for turbulent flow depends on the Reynold’s number and the pipe roughness. Figure 5.6 shows a Moody chart which shows the friction coefficient f as function of Reynold’s number and surface roughness for laminar and turbulent flows. Figure 5.
Table 5.2 shows the roughness for different materials. The friction increases in old pipes because of corrosion and sediments. Materials PVC Ploss, mechanical = Ploss, bearing + Ploss, shaft seal = constant Pipe in aluminium, copper og brass Table 5.2: Roughness for different surfaces (Pumpeståbi, 2000). Roughness k [mm] 0.01-0.05 (5.1) 0-0.003 0.01-0.05 V2 (5.2) 2g Welded steel pipe, new 0.03-0.15 Ploss, mechanical = Ploss, bearing + Ploss, shaft seal = constant 0.15-0.30 (5.
5. Pump losses Ploss, mechanical = Ploss, bearing + Ploss, shaft seal = constant (5.1) V2 5.3.2 Mixing loss at cross-section expansion H loss, friktion = ζ ⋅ H dyn, in = ζ ⋅ (5.2) 2g pressure energy at cross-section exVelocity energy is transformed to static 2 pansions in the pump, the energy equation in formula (2.10). The converLVsee H loss, pipe = f (5.3) sion is associated with Dh 2agmixing loss. 4A (5.4) Dh = is The reason O that velocity differences occur when the cross-section exVD h 5.7.
Pipe loss: H loss, pipe = f 2m ⋅ ( 3.45 m s) 2 LV 2 = 0.031 = 1.2 m 2 D h 2g 0.032m ⋅ 2 ⋅ 9.81 m s (5.7) V 12 (5.8) = ζ ⋅ = ζ ⋅ H H loss, expansion For a sudden expansion, as dyn,1 shown in figure 2 g 5.7, the following expression is used: A ζ = 1 − 1 A 2 2 (5.9) 2 where A V2 (5.10) H loss, contraction = 1 − 0 ⋅ 2 0 A1= Cross-section areaat inlet A 2 [m ]2 g A2= Cross-section area at outlet [m2] V 22 = ζ ⋅ = ζ ⋅ H H (5.
Relative roughness: k/Dh = 32mm = 0.0047 Q (10/3600) m3 s 2 Mean velocity: V = = = ⋅ 3.45 2m ( 3.45mmss) 2 5. Pump 0.0312 m2 = 1.2 m Pipe losses loss: H loss, pipe = Af LV π =0.032 2 D h 2 g4 0.032m ⋅ 2 ⋅ 9.81 m s 3.45m s ⋅ 0.032m VD h = 110500 Model Reynolds number: Re = ν =2 1 ⋅ 10 −6 m 2 s V1 (5.8)from V = ζ ⋅ that the acceleration of the fluid H loss, H dyn,1 Based on experience, assumed expansion = ζit⋅ is 1 2g 0.
5.3.4 Recirculation loss Recirculation zones in the hydraulic components typically occur at part load when the flow is below the design flow. Figure 5.10 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.
Dh 2 g Dh = 4 A O 5. Pump losses VD h Re = ν 64 flaminar = Re (5.4) (5.5) (5.6) Q (10/3600) m3 s Mean velocity: = 3.45 m s 5.3.5 Incidence loss V = A = π 0.032 2 m2 4 a difference between the flow angle and Incidence loss occurs when there is blade angle at the impeller or guide leading edges. This is typically the 3.45m s ⋅ 0.032m VD h vane = 110500 = =exists. −6 case at Reynolds part loadnumber: or when Re prerotation ν 1 ⋅ 10 m 2 s 0.
2 A V2 H loss, contraction = 1 − 0 ⋅ 0 2g A2 (5.10) V 22 (5.11) 2g Incidence loss is alternatively modelled as a parabola with minimum at the 2 2 w 1 − w 1, kanal w s best efficiency point. loss increases quadratically with = ϕThe incidence =ϕ H loss, incidence (5.12)the dif2 ⋅ g flow and 2the ⋅ g actual flow, see figure 5.13.
0.15mm Relative roughness: k/Dh = 2 = 0.0047 V 232mm H loss, contraction = ζ ⋅ H dyn,2 = ζ ⋅ 2g 5. Pump losses (5.11) 2 2 2m ⋅ ( 3.45 m s ) LV 2w =−0.031 w 1, kanal = 1.2 m Pipe loss: H loss, pipe w s=2 f D 2 g 1 2 = ϕh H loss, incidence = ϕ 0.032m ⋅ 2 ⋅ 9.81 m s (5.12) 2 ⋅g 2⋅g (5.7) Model Pfleiderer Petermann (1990, p. 2 322) use the following model to deter(5.13) H loss,and incidence = k 1 ⋅ ( Q − Q design ) + V 1k2 2 mine the increased power consumption caused by disk friction: (5.
2ν ⋅ 10 6 (5.14) k = 7.3 ⋅ 10 − 4 U DQ (10/3600) m3 s Mean velocity: V =2 2 = = 3.45 m s A 3 5π 0.032 2 m2 (n D24)A (Ploss, disk )A = ( Ploss, disk )B (5.15) (n3D52 )B 3.45m s ⋅ 0.032m VD h = 110500 Reynolds number: Re = = ν 1 ⋅ 10 −6 m 2 s (5.16) Q impeller = Q + Q leakage ( D22 −D2gap ) (5.17) H stat, gap =roughness: H stat, impeller −k/D ωh2fl = 0.15mm = 0.0047 where Relative 8g 32mm Qimpeller = Flow through impeller [m3/s], Q = Flow through pump [m3/s] , Qleakage V 2 + f L V 2 2+ 1.
2 2g 2m ⋅ ( 3.45 m s) 2 = 1.2 m Pipe loss: H loss, pipe = f LV = 0.031 2 D h 2g 2 0.032m ⋅ 2 ⋅ 9.81 m s 2 w − w w 1 1, kanal = ϕ s =ϕ H loss, incidence (5.12) 5. Pump losses 2 ⋅g 2⋅g V2 = ζ )⋅2 + 1k H H dyn,1 expansion==kζ⋅ ⋅( Q Hloss, − Q loss, incidence 1 design 2 g2 (5.7) (5.8) (5.13) where 2 Rotational A1 3 velocity of the fluid in the cavity between impeller ωfl = 1 ζ = − Ploss, disk (5.
5.4 Loss distribution as function of specific speed The ratio between the described mechanical and hydraulic losses depends on the specific speed nq, which describes the shape of the impeller, see section 4.6. Figure 5.18 shows how the losses are distributed at the design point (Ludwig et al., 2002). Flow friction and mixing loss are significant for all specific speeds and are the dominant loss type for higher specific speeds (semi-axial and axial impellers).
Chapter 6 Pump tests 6.1 Test types 6.2 Measuring pump performance 6.3 Measurement of the pump’s NPSH Hloss,friction,2 6.4 Measurement of force H U22 2.g 6.5 Uncertainty in measurement of performance 6.6 Summary U'22 2.g z'M2 Hloss,friction,1 U'12 2.g pM2 U12 2.g p'2 r.g p2 r.g pM1 p'1 r.g z'M1 p1 r.
6. Pump tests 6. Pump tests This chapter describes the types of tests Grundfos continuosly performs on pumps and their hydraulic components. The tests are made on prototypes in development projects and for maintenance and final inspection of produced pumps. 6.1 Test types For characterisation of a pump or one of its hydraulic parts, flow, head, power consumption, NPSH and force impact are measured. When testing a complete pump, i.e.
6.2 Measuring pump performance Pump performance is usually described by curves of measured head and power consumption versus measured flow, see figure 6.2. From these measured curves, an efficiency curve can be calculated. The measured pump performance is used in development projects for verification of computer models and to show that the pump meets the specification. During production, the performance curves are measured to be sure they correspond to the catalogue curves within standard tolerances.
6. Pump tests Grundfos builds test benches according to in-house standards where GS241A0540 is the most significant. The test itself is in accordance with the international standard ISO 9906. 6.2.1 Flow To measure the flow, Grundfos uses magnetic inductive flowmeters. These are integrated in the test bench according to the in-house standard. Other flow measuring techniques based on orifice, vortex meters, and turbine wheels exist. 6.2.
The pressure taps are designed so that the velocity in the pipe affects the static pressure measurement the least possible. To balance a possible bias in the velocity profile, each pressure tab has four measuring holes so that the measured pressure will be an average, see figure 6.4. Pressure gauge Venting Dz The measuring holes are drilled perpendicular in the pipe wall making them perpendicular to the flow.
6. Pump tests Figure 6.6: Draft of pump test on a piping. H2 H loss,friction, 2 H 2' H H' 1 H loss,friction,1 H1 S1' 6.2.4 Calculation of head The head can be calculated when flow, pressure, fluid type, temperature and geometric sizes such as pipe diameter, distances and heights are known. The total head from flange to flange is defined by the following equation: H = H2 − H1 (6.1) (6.2) H = ( H2' + H loss, friction,2 ) − ( H '1 − Hloss, friction,1 ) Figure 6.6 shows where the measurements are made.
S' 1 Figure 6.7: Pump test where the pipes are at an angle compared to horizontal. S1 Total head S1 S2 H' 1 U 12 2.g p1 r.g p' 2 r.g p2 r.g H1 2 U' 2 2.g H2 H' 2 z' 2 H = H2 − H1 S' 1 S' 2 2 z' 2 Because the manometer only measures the static pressure, the dynamic pressure must also be taken into acz' 1 count. The dynamic pressure depends on the pipe diamz1 eter and can be different on eachz2side of the pump. S' S1 S' 1 illustrates 2 2 a pump test in Figure 6.8 the basic Sversion of a pipe.
6. Pump tests 6.2.6 Power consumption Distinction is made between measurement of the shaft power P2 and added electric power P1. The shaft power can best be determined as the product of measured angular velocity w and the torque on the shaft which is measured by means of a torque measuring device. The shaft power can alternatively be measured on the basis of P1. However, this implies that the motor characteristic is known.
6.3 Measurement of the pump’s NPSH The NPSH test measures the lowest absolute pressure at the inlet before cavitation occurs for a given flow and a specific fluid with vapour pressure pvapour , see section 2.10 and formula (2.16). A typical sign of incipient cavitation is a higher noise level than usual. If the cavitation increases, it affects the pump head and flow which both typically decrease. Increased cavitation can also be seen as a drop in flow at constant head.
6. Pump tests 6.3.1 NPSH3% test by lowering the inlet pressure When the NPSH3% curve is flat, this type of NPSH3% test is the best suited. The NPSH3% test is made by keeping the flow fixed while the inlet pressure pstat,in and thereby NPSHA is gradually lowered until the head is reduced with more than 3%. The resulting NPSHA value for the last measuring point before the head drops below the 3% curve then states a value for NPSH3% at the given flow.
6.3.2 NPSH3% test by increasing the flow For NPSH3% test where the NPSH3% curve is steep, this procedure is preferable. This type of NPSH3% test is also well suited for cases where it is difficult to change the inlet pressure e.g. an open test stand. H The NPSH3% test is made by keeping a constant inlet pressure, constant water level or constant setting of the regulation valve before the pump. Then the flow can be increased from shutoff until the head can be measured below the 3% curve, see figure 6.10.
6. Pump tests In an open test bed, see figure 6.12, it is possible to adjust the inlet pressure in two ways: Either the water level in the well can be changed, or a valve can be inserted before the pump. The flow can be controlled by changing the pump’s counter-pressure by means of a valve mounted after the pump. Adjustable water level for flow valve and flow meter Pump 6.3.4 Water quality If there is dissolved air in the water, this affects the pump performance which can be mistaken for cavitation.
p' U '2 H = z 2' + M 2 + z 'M 2 + 2 + H loss, friction, 2 − ρ⋅g g 2 ⋅ p'M1 U1'2 − H loss, friction,1 (6.4) + z'M1 + 6.3.7 Barometric z 1' +pressure ρ⋅g 2⋅g In practise the inlet pressure is measured as a relative pressure in relation to the surroundings. It is therefore necesarry to know the barometric pressure at the place and time where the test is made. 6.3.
6. Pump tests 6.4.1 Measuring system The force measurement is made by absorbing the forces on the rotating system (impeller and shaft) through a measuring system. Dynamometer Axial bearing The axial force can e.g. be measured by moving the axial bearing outside the motor and mount it on a dynamometer, see figure 6.15. The axial forces occuring during operation are absorbed in the bearing and can thereby be measured with a dynamometer.
6.4.2 Execution of force measurement During force measurement the pump is mounted in a test bed, and the test is made in the exact same way as a QH test. The force measurements are made simultaneously with a QH test. At the one end, the shaft is affected by the pressure in the pump, and in the other end it is affected by the pressure outside the pump. Therefore the system pressure has influence on the size of the axial force.
to convert the measuring results to a constant fluid temperature and a constant speed. To ensure a measuring result which is representative for the pump, the test bed takes up more measurements and calculates an average value. ISO09906 has an instruction of how the test makes a representative average value seen from a stability criteria. The stability criteria is a simplified way to work with statistical normal distribution. 6.5.
Appendix Appendix A. Units Appendix B.
A. Units A. Units Some of the SI system’s units Basic Basicunits units Unit for Name Unit Length meter m Mass kilogram kg Time second S Temperature Kelvin K Unit for Name Unit Definition Angle radian rad One radian is the angle subtended at the centre of a circle by an arc of circumference that is equal in length to the radius of the circle..
Conversion of units Length m in (inches) ft (feet) 1 39.37 3.28 0.0254 1 0.0833 s min h (hour) 1 16.6667 . 10-3 0.277778 . 10-3 60 1 16.6667 . 10-3 3600 60 1 m3/h l/s gpm (US) 3600 1000 15852 0.277778 . 10 1 0.277778 4.4 10 3.6 1 15.852 0.2271 0.063 1 Time Flow, volume flow m3/s 1 -3 -3 0.000063 Mass flow Speed kg/s kg/h kg/s kg/h ft/s 1 3600 1 3600 3.28 1 0.277778 . 10-3 1 0.9119 0.3048 1.097 1 0.277778 .
A. Units Rotational speed RPM = revolution per minute s-1 rad/s 1 16.67 . 10-3 0.105 60 1 6.28 9.55 0.1592 1 kPa bar mVs 1 0.01 0.102 100 1 10.197 9.807 98.07 . 10-3 1 Pressure Work, energy Temperature K 1 o C J kWh t(oC) = T - 273.15K 1 0.277778 . 10-6 3.6 . 106 1 T(Kelvin) = 273.15 C + t 1 o Kinematic viscosity 116 Dynamic viscosity m /s cSt Pa .
B. Check of test results B. Check of test results When unexpected test results occur, it can be difficult to find out why. Is the tested pump in reality not the one we thought? Is the test bed not measuring correctly? Is the test which we compare with not reliable? Have some units been swaped during the data treatment? Typical examples which deviate from what is expected is presented on the following pages.
B. Check of test results Table 1: The test shows that the power consumption for a produced pump lies above the catalogue value but the head is the same as the catalogue curve. 118 Possible cause What to examine How to find the error The catalogue curve does not reflect the 0-series testen. Compare 0-series test with catalog curve If the catalogue curve and 0-series test do not correspond, it can not be expected that the pump performs according to the catalogue curve.
Table 2: The test shows that the power consumption and head lies below the catalogue curve. Possible cause What to examine How to find the error Curves have been made at different speeds. Find the speed for the catalogue curve and the test. Convert to the same speed and compare again. The catalogue curve does not reflect the 0-series test. Compare the 0-series test with the catalogue curve.
B. Check of test results Table 3: The power consumption is as the catalogue curve but the head is too low. 120 Possible cause What to examine How to find the error The catalogue curve does not reflect the 0-series test. Compare O-series test with catalogue curve. If the catalogue curve and 0-series test do not correspond, it can not be expected that the pump performs according to the catalogue curve. Increased hydraulic friction Compare the QH curves at the same speed.
Table 3 (continued) Possible cause What to examine How to find the error Increased leak loss. Compare QH curves and power Replace the impeller seal. curves. If the curve is a horizontal Close all unwanted circuits. displacement which decreases when the head (the pressure difference above the gap) falls, there could be an increased leak l oss. Leak loss is described in section 5.3.7. Measure the sealing diameter on the rotating and fixed part. Compare the results with the specifications on the drawing.
Bibliography European Association of Pump Manufacturers (1999), ”NPSH for rotordynamic pumps: a reference guide”, 1st edition. R. Fox and A. McDonald (1998), ”Introduction to Fluid Mechanics”. 5. edition, John Wiley & Sons. J. Gulich (2004), ”Kreiselpumpen. Handbuch für Entwicklung, Anlagenplanung und Betrieb”. 2nd edition, Springer Verlag. C. Pfleiderer and H. Petermann (1990), ”Strömungsmachinen”. 6. edition, Springer Verlag, Berlin. A.
Standards ISO 9906 Rotodynamic pumps – Hydraulic performance acceptance testGrades 1 and 2. The standard deals with hydraulic tests and contains instructions of data treatment and making of test equipment. ISO2548 has been replaced by ISO9906 ISO3555 has been replaced by ISO9906 ISO 5198 Pumps – Centrifugal-, mixed flow – and axial pumps – Hydraulic function test – Precision class GS 241A0540 Test benches and test equipment. Grundfos standards for contruction and rebuilding of test benches and data loggers.
Index A Absolute flow angle............................................................................. 61 Absolute pressure. .................................................................................33 Absolute pressure sensor..................................................................33 Absolute temperature.........................................................................33 Absolute velocity . .................................................................................
Efficiency...................................................................................................... 39 Electrical motor........................................................................................17 Electrical power. ................................................................................... 104 End-suction pump..................................................................................14 Energy class. ....................................................................
Index Moody chart.............................................................................................. 84 Motor. .............................................................................................................17 Motor characteristics..........................................................................98 N Non-return valve.....................................................................................51 NPSH . ..................................................................
Return channel.........................................................................................23 Reynolds’ number. ................................................................................ 83 Ring area...................................................................................................... 62 Ring diffusor...............................................................................................22 Rotational speed..............................................................
Index Velocity triangles.............................................................................60, 75 Volute. ............................................................................................................22 Volute casing.............................................................................................21 Vortex pump............................................................................................. 16 W Water quality. ..................................................
List of Symbols Symbol Definition FLOW Q Flow, volume flow Design flow Qdesign Flow through the impeller Qimpeller Leak flow Qleak m Mass flow Unit [m3/s] [m3/s] [m3/s] [m3/s] [kg/s] HEAD H Head [m] Hloss,{loss type} Head loss in {loss type} [m] NPSH Net Positive Suction Head [m] NPSHA NPSH Available (Net Positive Suction Head available in system) [m] NPSH Required (The pump’s net positive suction head system demands) [m] NPSHR, NPSH3% GEOMETRIC DIMENSIONS A Cross-section area
Affinity rules Physical properties for water T [°C] pvapour [105 Pa] r [kg/m3] n [10-6 m2/s] 0 0.00611 1000.0 1.792 4 0.00813 1000.0 1.568 1.307 10 0.01227 999.7 20 0.02337 998.2 1.004 25 0.03166 997.1 0.893 30 0.04241 995.7 0.801 40 0.07375 992.3 0.658 50 0.12335 988.1 0.554 60 0.19920 983.2 0.475 70 0.31162 977.8 0.413 80 0.47360 971.7 0.365 90 0.70109 965.2 0.326 100 1.01325 958.2 0.294 110 1.43266 950.8 0.268 120 1.98543 943.0 0.246 130 2.
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