sign in sign up
<<
Home , Francis turbine, Turbomachinery

Fluid Machinery

ME 306 Fluid Mechanics II • Fluid machinery is used to convert hydraulic to mechanical energy or vice versa.

Part 3 Power absorbing Power producing Work is done on the fluid Work is done by the fluid Mechanical Energy → Hydraulic Energy Hydraulic Energy → Mechanical Energy

These presentations are prepared by Dr. Cüneyt Sert Department of Middle East Technical University Ankara, Turkey [email protected]

Please ask for permission before using them. You are NOT allowed to modify them. 3-1 3-2

Classification of Fluid Machinery Classification of Fluid Machinery (cont’d)

• Fluid machinery can be classified based on the motion of moving parts. 2 ) Turbomachines 1 ) Positive Displacement • Turbo means ‘‘spin’’ or ‘‘whirl’’ in Latin. • Fluid is directed into a closed volume. • Turbomachines use rotating shafts with attached blades, vanes, buckets, etc. • Energy transfer is accomplished by movement of the boundary of the closed • In ME 306 we’ll study turbomachines, mostly . volume. • Closed volume expands and contracts, sucking the fluid in or pushing it out.

http://www.britannica.com http://www.noehill.com/ http://en.wikipedia.org nevada_county_california http://speakeasies.biz http://www.bicycleaccessories.us http://en.wikipedia.org /cal1012.asp Kaplan type Axial Centrifugal pump Human heart Water well pump Tire pump Gear pump hydraulic turbine 3-3 3-4 Classification of Turbomachines Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Incompressible Compressible Incompressible Compressible Incompressible Compressible Incompressible Compressible

Pump Pump Propeller

• Propellers are used to generate thrust. • Pumps increase the pressure of a liquid without changing its velocity considerably. • Marine propellers work with incompressible water and aircraft propellers work with • Shown centrifugal (radial) pump is the most compressible air. common type. • Pressure difference between the front and back • Visit www.standartpompa.com to get more surfaces of the blades create the thrust. information on sizes and capacities.

3-5 3-6

Classification of Turbomachines (cont’d) Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Incompressible Compressible Incompressible Compressible Incompressible Compressible Incompressible Compressible

Pump Propeller Fan Pump Propeller Fan Blower

• The main difference between fans, blowers and is the pressure difference they • create. Blowers work with medium amout of flow rates and pressure ratios. • Fans create small pressure difference. Their main • purpose is to put high amount of fluid into They are mostly centrifugal type. motion. • Shown is an industrial type blower. • Shown is axial fan of a wind tunnel. 3-7 3-8 Classification of Turbomachines (cont’d) Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Incompressible Compressible Incompressible Compressible Incompressible Compressible Incompressible Compressible

Pump Propeller Fan Blower Pump Propeller Fan Blower Compressor Pelton wheel

• Compressors work with smaller flow rates, but • Pelton wheels have buckets attached to a create very high pressure ratios. rotating disk (wheel). • Shown is a multi-stage . • They convert kinetic energy of a high speed liquid jet into mechanical energy. • Compressors are used in gas and steam , natural gas pumping stations, , • Largest ones used at hydraulic power plants have refrigeration cycles, etc. capacities up to 200 MW.

3-9 3-10

Classification of Turbomachines (cont’d) Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Incompressible Compressible Incompressible Compressible Incompressible Compressible Incompressible Compressible

Pump Propeller Fan Blower Compressor Pelton Hydraulic Pump Propeller Fan Blower Compressor Pelton Hydraulic Steam wheel turbine wheel turbine turbine

• Hydraulic turbines are used at to generate • Steam turbines are used at power plants to electricity using high pressure water. generate electricity using high temperature and high pressure steam. • Common types are Francis and Kaplan. • 80 % of world’s electricity is produced by steam • Shown are the runner blades of the Francis turbines. turbines used at Three Gorges / China. • Afşin-Elbistan thermal power plant has a • Atatürk Dam has a capacity of 8 x 300 MW. capacity of 4 x 344 MW. 3-11 3-12 Classification of Turbomachines (cont’d) Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Incompressible Compressible Incompressible Compressible Incompressible Compressible Incompressible Compressible

Pump Propeller Fan Blower Compressor Pelton Hydraulic Steam Gas Pump Propeller Fan Blower Compressor Pelton Hydraulic Steam Gas Wind wheel turbine turbine turbine wheel turbine turbine turbine turbine

• Gas turbines are similar to steam turbines, but • As of 2017 Turkey’s wind energy production is they use high temperature and high pressure 6 GW. Total available capacity is 48 GW. combustion gases. • World’s total wind energy production is 490 GW, • A Boeing 777 is powered by 2 , which is about 2.5 % of all electricity usage. each generting a thrust of ~500 kN. • There are wind turbines with more than 120 m • To learn how a turbofan operates visit rotor diameter, producing 6 MW of electricity http://www.youtube.com/watch?v=GpklBS3s7iU (enough for 4500 homes) (http://www.youtube.com/watch?v=LQxp6QTjgJg) 3-13 3-14

Another Classification of Turbomachines Another Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Uncased Cased Impulse Reaction Uncased Cased Impulse Reaction

Axial Flow Axial Flow Axial Propeller Propeller

Out • Fluid enters an axial flow turbomachine parallel • Uncased turbomachines do not have a solid to the axis of rotation. casing around them. • Fluid leaves the also in axial direction.

In

3-15 3-16 Another Classification of Turbomachines (cont’d) Another Classification of Turbomachines (cont’d) Turbomachines Turbomachines

Power absorbing Power producing Power absorbing Power producing

Uncased Cased Impulse Reaction Uncased Cased Impulse Reaction

Axial Flow Axial Radial Axial Flow Axial Radial Mixed Pelton Wind Axial Propeller Propeller wheel turbine (Kaplan)

In • Kaplan turbines are axial flow machines. • In radial flow machines fluid intake is parallel to In In Out the axis of rotation. • They are preferred for low head and high flow • Rotating impeller blades push the fluid in radial rate configurations. direction. • Their capacities are less than Francis type, less • Fluid leaves the machine perpendicular to the than 200 MW. rotation axis. Out Out • They can provide efficiencies higher than 95 %. 3-17 3-18

Another Classification of Turbomachines (cont’d) Centrifugal Pump

Turbomachines • Centrifugal pump is the most commonly used type of turbomachine.

Power absorbing Power producing Discharge (outflow) Uncased Cased Impulse Reaction Impeller Hub Axial Flow Axial Radial Mixed Pelton Wind Axial Radial Mixed Propeller wheel turbine (Kaplan) (Banki) (Francis) Eye

• Francis turbines are the most widely used Inflow turbomachines for . Blade Munson • They are of mixed flow type. Casing, housing • They can provide more than 800 MW power. or volute • For more information http://www.voithhydro.com 3-19 3-20 Centrifugal Pump (cont’d) Pump Head (ℎ푠)

• For centrifugal pump details watch 푝표푢푡

http://www.youtube.com/watch?v=9nL1XhKm9q8 (Principles and parts) 푄 푉표푢푡 http://www.youtube.com/watch?v=Vq3hEe5jzSM (Pump Parts) 푝 퐴표푢푡 http://www.youtube.com/watch?v=UrChdDwHybY (Impeller animation) 𝑖푛 푉𝑖푛 푄 http://www.youtube.com/watch?v=RvOzKhUDmJM (Computer aided blade design) 푧 퐴𝑖푛 • Most important part is the impeller. It may have different designs such as Datum • Backward-curved, radial or forward-curved • Consider the BE between the inlet (suction) and outlet (discharge) of a pump. • Closed (shrouded) or open 2 2 Open, radial Closed (Shrouded) 푝𝑖푛 푉𝑖푛 푝표푢푡 푉표푢푡 + + 푧𝑖푛 = + + 푧표푢푡 − ℎ푠 Open 휌푔 2푔 휌푔 2푔 Pump head • Pump head is the difference between the total heads at the pump inlet and outlet. Called backward- Called forward- curved if rotates in curved if rotates • Pump head is a positive quantity with units of length. this direction in this direction 3-21 3-22

Pump Head (cont’d) Theoretical Analysis of a Centrifugal Pump

• Elevation difference between inlet and outlet is generally negligibly small. Exercise: Consider the given schematic of a centrifugal pump. Perform a control volume analysis to derive a relation for the variation of the theoretical (ideal) pump • If suction and discharge pipe diameters are the same → 푉 = 푉 𝑖푛 표푢푡 head as a function of discharge (volumetric flow rate). • For this simplified case 푝 − 푝 ∆푝 Out ℎ = 표푢푡 𝑖푛 = 푠 휌푔 휌푔 훽2 i.e. pump head is the pressure rise across the pump expressed as a head. 푏 훽1 푟2

• Pump head is directly related to the power delivered to the fluid, known as water In 푟1 휔 1 Inlet horsepower 1 In 2 Outlet 풫푓 = 휌푔푄 ℎ푠 2

푓 for fluid Weight flow rate Blade

• Pump head can be defined as the power delivered to the fluid per weight of the fluid Out flowing through the pump in unit time (weight flow rate). 3-23 3-24 Theoretical Analysis of a Centrifugal Pump (cont’d) Pump Efficiency

Exercise: Water is pumped at a rate of 5300 L/min through a centrifugal pump • Power necessary to run the pump (풫푝), known as brake horsepower (bhp), is larger operating at 1750 rpm. The impeller has a uniform blade height, 푏, of 5 cm with than power delivered to the fluid due to 푟 = 4 cm and 푟 = 18 cm, and exit blade angle 훽 is 23o. Assume ideal flow 1 2 2 • mechanical and fluidic frictional losses conditions and the tangential velocity component, 푉1휃, of the water entering the blade is zero. Determine • flow separation on impeller blade surfaces

a) the tangential velocity component, 푉2휃, at the blade exit. • misalignment of inlet flow velocity with impeller blade geometry b) the ideal head rise • internal leakage, etc. c) the power transferred to the fluid. 풫푝 = 푇푠ℎ푎푓푡 휔 > 풫푓 Reference : Munson 푝 for pump Rotational speed Torque supplied to of the pump the pump shaft

• Efficiency of the pump is defined as

풫푓 휂푝 = < 1 풫푝 3-25 3-26

Pump Efficiency (cont’d) Important Parameters of a Centrifugal Pump

풫푓 휂 = 풫 (풫 ) : Pump power. Also called shaft • Volumetric flow rate (discharge, capacity) 푄 푝 풫 푝 푠ℎ 푝 power. Power input to the pump. • Head ℎ푠 (or simply ℎ) 풫 풫 𝑖 푓 풫𝑖 : Internal power 휂푚 = 휂𝑖 = = 휂ℎ휂푣 • Size (impeller diameter) 퐷 풫푝 풫𝑖 풫푓 : Fluid power. Power delivered to the fluid. • Rotational speed 푁 [rpm] or 휔 [s-1]

Pump • Power consumption 풫푝 풫푙 : Mechanical power loss at bearings, etc. • Efficiency 휂푝 (or simply 휂) ℎ푙 : Hydraulic friction loss (head loss) 풫푝 (풫푠ℎ) 풫𝑖 풫푓 푄퐿 : Leakage loss ℎ 휂 휂푚 : Mechanical efficiency • Fundamental characteristic curve of a pump 휂 = 휂 휂 : Internal efficiency 𝑖 ℎ 푣 is a plot of ℎ vs. 푄 at a given rotational speed 휔. (Hydraulic eff. x Volumetric eff.) 풫푝 풫푙 ℎ푙 푄퐿 • It is customary to plot 풫푝 and 휂 on the same figure. 휂푝 = 휂푚휂ℎ휂푣 : Pump (overall) efficiency 푄 3-27 3-28 Pump Characteristic Curve Best Efficiency Point (BEP)

• ℎ − 푄 curve of a pump is known as its characteristic curve. • The exact operation point of a pump depends on the system it is working in. • A pump can operate only on its characteristic curve. • Pumps are designed to work at (or close to) their maximum efficiency, but this is not always possible. • At a given rotational speed (휔) a typical centrifugal pump characteristic curve is Best Efficiency Point (BEP) (or design point) Shutoff head ℎ Head (ℎ) • Discharge valve of Efficiency (휂) the pump is closed Free delivery ℎ for maximum and 푄 = 0. efficiency • There is no load • Pump is not doing on the pump and any useful work. ℎ = 0. • 풫 = 0 & 휂 = 0 푓 • Pump is not doing Power (풫푝) any useful work Note: All these • 풫푓 = 0 & 휂 = 0 푄 Note : This curve is for a curves are for a given given rotational speed. 휔 푄 rotational speed . 푄 for maximum efficiency 3-29 3-30

System Characteristic System Characteristic (cont’d)

• A pump works at an operating point on its characteristic curve. • ℎ푓 consists of major and minor losses calculated as • But this operating point depends on the system that the pump is installed in. Actual or equivalent pipe length • 푠푟 푑푟 2 2 Following pump works between a suction reservoir ( ) and a discharge reservoir ( ). 퐿𝑖 푉𝑖 푉𝑖 ℎ푓 = 푓𝑖 + 푘𝑖 퐷𝑖 2푔 2푔 𝑖 𝑖 • BE between points 푠푟 and 푝푟 Head loss coefficient 푝푑푟 Friction factor Pipe diameter 푝 푉2 푝 푉2 for minor losses 푠푟 + 푠푟 + 푧 = 푑푟 + 푑푟 + 푧 − ℎ + ℎ 휌푔 2푔 푠푟 휌푔 2푔 푑푟 푓 • 푉𝑖’s are average velocities in suction and discharge pipes. ℎ푔푡 Total major and • Using the continuity eqution 푉𝑖 = 푄/퐴𝑖 minor losses 푝 Pump 푠푟 and the total loss becomes

• If 푝푠푟 = 푝푑푟 = 푝푎푡푚 and 푉푠푟 = 푉푑푟 = 0 2 2 퐿𝑖 푄 푄 ℎ푓 = 푓𝑖 2 + 푘𝑖 2 퐷𝑖 2푔퐴𝑖 2푔퐴𝑖 ℎ = ℎ푔푡 + ℎ푓 𝑖 𝑖

2 or simply ℎ푓 = 퐾푄 Total geometric head (= 푧푑푟 − 푧푠푟) 3-31 3-32 System Characteristic (cont’d) System Characteristic (cont’d)

• Using this ℎ푓 in the BE we get the following system characteristic equation • It is possible to change system characteristic in two ways.

2 ℎ = ℎ푔푡 + 퐾푄 Total geometric head (ℎ푔푡, the Friction loss can be changed by difference between reservoir levels) changing 퐾. For example by opening ℎ 2 can be changed. or closing a valve. ℎ푔푡 + 퐾푄

ℎ + 퐾푄2 푔푡3 ℎ + 퐾 푄2 ℎ푔푡 ℎ ℎ 푔푡 3 2 ℎ푔푡 + 퐾푄 2 2 ℎ푔푡 + 퐾2푄 푄 ℎ + 퐾푄2 푔푡1 2 ℎ푔푡 + 퐾1푄

• Minimum head the pump should provide is equal to the total geometric head. 퐾 increases • Additional pump head is necessary to overcome frictional losses. This part increases ℎ푔푡 increases with the square of the flow rate. 푄 푄

3-33 3-34

Operating Point Operating Point (cont’d)

• A pump installed on a system will not work at an arbitrary point. Exercise: Water is pumped from one large open tank to a second one. The pipe diameter throughout is 15 cm and the total length of the pipe between the pipe • It will operate at the point where pump and system characteristics intersect. entrance and the exit is 60 m. Minor loss coefficients for the entrance, exit and the elbow are shown and the friction factor for the pipe can be taken as 0.02. A certain Operating centrifugal pump with the shown characteristic is suggested for this flow system. ℎ point System characteristic With this pump, what would be the flow rate? Do you think this pump is a good (Demand curve) choice? (Reference: Munson) 100 30 ℎ표푝 80 24 Pump characteristic Pump (Supply curve) 60 18 3 m 푄 푘푒푥𝑖푡 = 1.0 40 12

푄표푝 Head [m] Efficiency [%] Efficiency 푘푒푙푏표푤 = 1.5 20 6 • Normally we want the operating point to be close to the BEP (design point). 푘 = 0.5 0 0 𝑖푛푙푒푡 0 1.5 3.0 4.5 6.0 7.5 9.0 • However BEP is not always the most economical operating point as far as the power Flow rate [m3/min] consumption is concerned, i.e. BEP is not necessarily the minimum 풫푝 point. 3-35 3-36 Similarity Laws for Pumps Similarity Laws for Pumps (cont’d)

• Similitude analysis is typically used • In most pump applications similarity of viscous forces are not as important as the other 휋 groups. • to predict the performance of a pump when a different sized impeller is used in the same casing. • Two geometrically similar pumps are said to be operating under similar conditions if the remaining three 휋 groups are equal. • to predict the performance of a pump when it operates at a different speed. 휋 = 휋 , 휋 = 휋 , 휋 = 휋 푄1 푄2 ℎ1 ℎ2 풫1 풫2 • Perform a Buckingham-Pi analysis with the following parameters Affinity laws 푄 , 푔ℎ , 퐷 , 풫푝 , 휔 , 휌 , 휇 to get the following non-dimensional groups where 1 and 2 are two similar operating points (homologous points).

푄 푔ℎ Exercise : Show that when affinity laws are satisfied, efficiencies of two homologous Flow coefficient : 휋 푄 = Head coefficient : 휋 = 휔퐷3 ℎ 휔2퐷2 points are equal.

Exercise : How does the nondimensional performance curve (휋 vs. 휋 ) of two 풫푝 휇 1 ℎ 푄 Power coefficient : 휋 = Reynolds number : 휋 = = 풫 휌휔3퐷5 휇 휌휔퐷2 푅푒 geometrically similar pumps compare with each other? What about 휋풫 vs. 휋푄 and 휂 vs. 휋푄 curves? 3-37 3-38

Similarity Case 1 – Different Rotational Speeds Similarity Case 1 (cont’d)

• Consider a pump with a known performance. We want to determine its operation at a Exercise : Head and efficiency of a centrifugal pump running at 1500 rpm are given as different speed. ℎ = 50 – 200 푄 – 24000 푄2 휂 = 60 푄 – 1200 푄2

퐷1 = 퐷2 It is desired to deliver 0.03 m3/s of water against a head of 36 m. Determine 휔1 ≠ 휔2 a) speed of the pump b) efficiency of the pump Point 2 Delivering 푄1 and ℎ1 Delivering 푄2 and ℎ2 (desired c) power consumption 60 Using 풫푝 Using 풫푝 operating point) 1 2 of the pump 50 3 푄2 = 0.03 m /s 40 ℎ2 = 36 m Point 1 ℎ [m] 30 푁2 = ? • Pump sizes are the same (퐷1 = 퐷2). Affinity laws are simplified as follows (a point similar to 20 point 2) 2 풫 3 푄1 휔1 ℎ1 휔1 푝1 휔1 10 = , = , = 푄1 = ? 푄2 휔2 ℎ2 휔2 풫푝 휔2 2 ℎ = ? 0 1 0 0.01 0.02 0.03 0.04 푁 = 1500 rpm 3 3-39 1 푄[m /s] 3-40 Similarity Case 2 – Different Sizes (Impeller Diameters) Similarity Case 2 (cont’d)

• Consider a pump with a known performance. We want to study the operation of a Exercise : Characteristic curve of a centrifugal pump is given as similar pump with a different impeller size rotating at the same speed. ℎ = 100 – 1000 푄2 It is desired to deliver 0.1 m3/s of water against a head of 70 m. For these requirements it is thought that using a similar pump with a smaller impeller would be 휔1 = 휔2 more efficient.

퐷1 ≠ 퐷2 a) Determine the required percent reduction in impeller diameter. b) Determine the percent decrease in power consumption. Delivering 푄1 and ℎ1 Delivering 푄2 and ℎ2 120 Using 풫 Using 풫 푝1 푝2 Point 2 100 Point 1 (desired (a point similar to 80 operating point) • Rotational speeds are the same (휔1 = 휔2). Affinity laws simplify as follows point 2) ℎ [m] 60 3 푄2 = 0.1 m /s 3 2 풫 5 푄1 = ? 40 ℎ = 70 m 푄1 퐷1 ℎ1 퐷1 푝1 퐷1 2 = , = , = ℎ = ? 퐷 = ? 푄 퐷 ℎ 퐷 풫 퐷 1 20 2 2 2 2 2 푝2 2 퐷1 = ? 0 3-41 0 0.1 푄 [ m 3 / s ] 0.2 0.3 3-42

System Characteristic, Operating Point & Similarity Series Combination of Pumps

Exercise : Characteristics of a centrifugal pump at 600 rpm is given below. The pump • Series combination is used if the head provided by a single pump is not enough. is used to elevate water by 32 m from a lake to an open tank. Flow rate is measured as 22 lps while the delivery valve is fully open and the pump running at 600 rpm.

70 Determine the power consumption 푄퐴 푄퐵 푄 = 푄퐴 = 푄퐵 for the following operations. 60 휂 [%]

a) Valve closure is increased 50 such that the frictional loss Pump A Pump B ℎ m provides ℎ Provides ℎ is doubled. 40 퐴 퐵

b) Pump speed is increased 30 ℎ = ℎ퐴 + ℎ퐵 to 720 rpm while keeping the valve fully open. 20 • Same 푄 goes through both pumps. • Total head provided is the sum of individual heads. 10 • Pumps can be identical or different. 0 0 10 20 30 40 50 • More than two pumps can be combined in series. 푄 [lps] 3-43 3-44 Series Combination of Pumps (cont’d) Series Combination of Pumps (cont’d)

Exercise : Show that for two pumps combined in series overall efficiency is • If the pumps are NOT identical ℎ + ℎ 휂 = 퐴 퐵 ℎ ℎ ℎ 퐴 + 퐵 System 휂 휂 Pump A+B 퐴 퐵 in series characteristic • To get combined pump characteristic, individual pump characteristics are added vertically. • ℎ Operating If the pumps are identical Pump A+B Pump A point in series System characteristic Pump B Operating 푄 point 푄푐

Pump A or B • Above a certain 푄푐 pump B is forced to operate above its free delivery point. For such a case it just creates extra loss and should be shut off and bypassed. 푄 3-45 3-46

Series Combination of Pumps (cont’d) Parallel Combination of Pumps

Exercise : Two identical pumps, with shown characteristics, are combined in series and • Parallel combination is used if the flow rate provided by a single pump is not enough. used to transport water between two reservoirs with an elevation difference of 푧 – 푧푠푟 = 50 m. Total length of suction and discharge pipes is 120 m. Pipe 푑푟 Pump A diameters are 0.12 m. Friction factor inside the pipes is 0.022. Neglecting the minor 푄퐴 losses, determine the power required to drive both pumps.

푄 = 푄퐴 + 푄퐵 90 푄퐵 70 Pump B

ℎ [m] 50 ℎ = ℎ퐴 = ℎ퐵 휂 [%] 30

10 • Each pump provides the same head ℎ. 0 0.01 0.02 0.03 0.04 0.05 • Total flow rate is the sum of individual flow rates. 푄 [m3/s] • Pumps can be identical or different. • More than two pumps can be combined in parallel. 3-47 3-48 Parallel Combination of Pumps (cont’d) Parallel Combination of Pumps (cont’d)

Exercise : Show that for two pumps combined in parallel overall efficiency is • If the pumps are NOT identical 푄 + 푄 휂 = 퐴 퐵 푄 푄 퐴 + 퐵 ℎ Operating 휂퐴 휂퐵 point System • To get combined pump characteristic, individual pump characteristics are added characteristic horizontally.

• If the pumps are identical ℎ ℎ푐 System Pump A+B Pump A+B characteristic in parallel in parallel Pump B Pump A 푄 Operating point • Above a certain ℎ푐 pump B is forced to operate above its shutoff head. For such a case Pump A or B it just creates extra loss and should be shut off and its branch should be blocked with a 푄 valve.

3-49 3-50

Cavitation Cavitation Damage

• In a liquid flow cavitation occurs when the local static pressure falls below the vapor Damage on pressure of the liquid. blades • For a cavitating flow • liquid locally vaporizes forming bubbles. Damage on centrifugal pump impeller • bubbles collapse as they travel to higher pressure regions and cause erosion/surface pitting. • flow becomes unsteady, causing noise and vibration. en.wikipedia.org • performance of the turbomachine drops.

• For a pump, critical low pressure region is the entrance, and for a turbine it is the exit. • High speed regions like propeller blade tips are also critical.

• Listen to the sound of a cavitating pump : www.youtube.com/watch?v=Qw97DkOYYrg Damage on • Watch propeller tip cavitation : www.youtube.com/watch?v=GpklBS3s7iU propeller www.pumpfundamentals.com en.wikipedia.org blades 3-51 3-52 Cavitation of a Pump and 푁푃푆퐻 NPSH (cont’d)

• Cavitation possibility of a pump is checked using Net Positive Suction Head (푁푃푆퐻). • There are two values of 푁푃푆퐻 that we work with

• 푁푃푆퐻 is the difference between the total head at the suction side and the head • 푁푃푆퐻 required (푁푃푆퐻푅) corresponding to the vapor pressure. • 푁푃푆퐻 available (푁푃푆퐻퐴) Suction velocity • 푁푃푆퐻푅 is the value that must be exceeded to prevent cavitation inside the pump. Suction pressure Vapor pressure • It is measured by the manufacturer of the pump and provided as an extra curve on the 푝 푉2 푝 pump characteristic plot. 푁푃푆퐻 = 푠 + 푠 − 푣 휌푔 2푔 휌푔 ℎ Total head at the suction side 휂 of the pump (Datum is arranged so that 푧푠 = 0)

• Point 푠 denotes the suction side (inlet) of the pump. 푁푃푆퐻푅 푁푃푆퐻푅 • It is used in the definition because it is the critical low pressure region.

3-53 푄 3-54

NPSH (cont’d) NPSH (cont’d)

푝푎푡푚 − 푝푣 • 푁푃푆퐻퐴 is the value that we need to calculate for the problem of interest. 푁푃푆퐻 = Provided by the manufacturer , 푁푃푆퐻 = − ℎ − 퐻 푅 퐴 휌푔 푓푠 푠 • Consider the BE for the suction side of a pump

2 2 푝푠푟 푉푠푟 푝푠 푉푠 • To prevent cavitation + + 푧푠푟 = + + 푧푠 + ℎ푓푠 No cavitation Cavitation 휌푔 2푔 휌푔 2푔 Pump 푁푃푆퐻퐴 ≥ 푁푃푆퐻푅 푠 푝푠푟 = 푝푎푡푚 ℎ Typically 푉 = 0 퐻푠 푠푟 푁푃푆퐻퐴 푠푟 푧 − 푧 = 퐻 푁푃푆퐻 푠 푠푟 푠 Suction pipe 푅 ℎ푓푠 : Frictional losses at the suction side of the system Exercise : What can be done to make 푁푃푆퐻퐴 larger for the pump shown in the previous slide? 푝 푉2 푝 푝 − 푝 푠 + 푠 = 푎푡푚 − ℎ − 퐻 → 푁푃푆퐻 = 푎푡푚 푣 − ℎ − 퐻 휌푔 2푔 휌푔 푓푠 푠 퐴 휌푔 푓푠 푠 Exercise : How does the vapor pressure of water change with temperature? What does this information tell us about preventing cavitation? 3-55 3-56 NPSH (cont’d) NPSH (cont’d)

Exercise : A centrifugal pump is to be placed above a large open water tank to pump Exercise : Centrifugal pump with the given characteristic is running at 1450 rpm to water at a flow rate of 1.4 × 10−2 m3/s. At this flow rate the required NPSH value is pump water at 25 ℃ from a reservoir whose surface is 1.2 m above the centerline of given as 4.5 m by the pump manufacturer. Water temperature is 30 oC and the the pump inlet. Reservoir is open to www.standartpompa.com atmospheric pressure is 95 kPa. Suction side pipe is short and the main head loss atmospheric pressure. between the suction tank and the pump is due to a filter that has a head loss 12 The piping system from the reservoir coefficient of 푘 = 20. Other losses can be neglected. Suction pipe diameter is 10 cm. to the pump consists of 3.2 m of cast 11 iron pipe with a diameter of 5 cm and a) Determine the maximum height that the pump can be located above the water 10

an average roughness of 0.05 cm. m surface of the suction tank without cavitation. 9 Minor losses at the suction side of the ℎ b) If you were required to place a valve in the flow path to regulate the flow rate, pump are; sharp edged inlet (푘 = 0.5), would you place it upstream or downstream of the pump? Why? 8 three flanged smooth 90o elbows (푘 = 0.3 each) and a fully open flanged 7 (Munson’s book) Filter globe valve (푘 = 6). 6 푠 Pump Estimate the maximum flow rate that 퐻 = ? m 2

푠 can be pumped without cavitation. 푅

푠푟 퐻 1

푃푆 0 N 0 2 4 6 8 10 12 14 16 18 3 3-57 푄 [m /h] 3-58

Pump (푁푠) Pump Specific Speed (cont’d)

• Specific speed is a useful non-dimensional pi-term obtained by combination 휋푄 and 푁푠푑 휋 to eliminate 퐷. 500 1000 2000 5000 10000 20000 ℎ 1 1/2 Centrifugal Mixed Axial 휋푄 휔 푄 0.9 푁푠 = 3/4 = 3/4 휋ℎ (푔ℎ) 0.8 휂max • In the industry the following dimensional form is also commonly used 0.7

휔(rpm) 푄(liter/min) 0.6 ( 푁푠푑 = 3/4 Note that g is missing) ℎ(m) 0.5 Çengel’s book 0.1 0.2 0.5 1 2 5 10 푁푠 where 푁푠푑 = 2733 푁푠

• Centrifugal (radial) pumps work efficiently at low specific speeds (푁푠 < 1.5).

• 푁푠 is useful to classify and compare different types of pumps at their BEP. • Mixed pumps work efficiently at medium specific speeds (1.5 < 푁푠 < 3.5).

• 푁푠 is mainly used for preliminary pump selection. • Axial (propeller) pumps work efficiently at high specific speeds (푁푠 > 3.5).

3-59 3-60 Axial Pumps (Propeller Pumps) Pump Selection

• Centrifugal pumps are usually work efficiently at high ℎ and low 푄. • Two main inputs for pump selection are • Certain applications, such as drainage and irrigation involve low ℎ and high 푄. • required head, ℎ. • required flow rate, 푄.

Flow Fixed stator (guide) vanes • Additional considerations for pump selection are coming in Rotating rotor blades • pump speed • type of fluid (highly viscous, muddy, etc.)

• available space, vertical placement limitations, etc. that will affect 푁푃푆퐻퐴 • maximum allowable noise level wikipedia.com Flow • etc. going out

• For preliminary pump selection specific speed (푁푠) is commonly used. • World’s most powerful pump: http://pressurewashr.com/the-worlds-most- powerful-water-pump/

3-61 3-62

Pump Selection (cont’d) Pump Selection (cont’d)

• Manufacturers provide catalogues of their pumps. • This one is for axial pumps produced by Goulds Pumps. • Following chart is for centrifugal pumps produced by Standart Pompa. • For an application with 푄 = 5000 m3/h and ℎ = 4 m, ‘‘24-24 24’’ family seems suitable. • For an application with 푄 = 100 m3/h and ℎ = 30 m, ‘‘65-160’’ family seems suitable.

12 100 www.gouldspump.com 80 10 60 8 40 ℎ m ℎ m 6 30 4

20 2

15 2900 rpm 0 600 1000 2000 3000 5000 8000 12000 20000 40000 www.standartpompa.com 10 3 5 10 20 30 40 50 100 200 300 600 푄 [m /h] 3 푄 [m /h] 3-63 3-64 Pump Selection (cont’d) 2900 rpm Turbines 휙 184 50 50% 60 65 • These are the detailed performance 45 70 휙 175 73.5 curves of the the pumps in the ‘‘65- 1000 www.3helixpower.com 40 Impulse Types 160’’ family of Standart Pompa. 휙 160 70 35 • There are three similar pumps with m 65 300 Pelton wheel ℎ 30 60 200 impeller diameters of 160 mm, Turgo 175 mm and 184 mm. 25 50 20 Cross-flow

• Red curves are iso-efficinecy lines. 50 m • 푁푃푆퐻 풫 10

and curves are also ℎ

푅 푝 푅 휙 160 휙 184

provided. 퐻 6 Reaction Types m 푃푆 2

N 10 • One of these three pumps can be Francis 20 selected by considering cavitation 휙 184 15 Kaplan possibility, efficiency and power 휙 175 2

consumption. kW 10 휙 160

푝 1 풫 5 • The smallest pump cannot provide the 0.2 0.5 1 2 10 50 100 Adapted from www.standartpompa.com required head of 30 m at the desired 0 3 0 20 40 60 80 100 120 140 푄 [m /s] flow rate of 100 m3/h. 3 푄 [m /h] 3-65 3-66

Turbines (cont’d) Turbine Specific Speed (푁푠푡) • Fundamental performance characteristic of a turbine is the power produced (풫 ) vs. 푡 1 rotational speed curve at a given head. Çengel’s book & www.repack-s.com Francis Kaplan Impulse 0.9 풫푡 0.8 휂max 0.7

At a given 0.6 head ℎ 푁 0.5 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 푁 • Affinity laws used for pumps are valid for turbines too. 푠푡

• Turbine specific speed can be used for preliminary turbine selection. It is defined in a • Impulse turbines work efficiently at low specific speed (푁푠 < 0.3) (High ℎ, low 푄). slightly different way than pumps 푡 • Francis turbines work efficiently at medium specific speeds (0.3 < 푁푠 < 2). 1/2 푡 휋풫 휔 풫푡 푁푠푡 = 5/4 = 5/4 • Kaplan turbines work efficiently at high specific speeds (푁푠 > 2) (Low ℎ, high 푄). 휋ℎ 휌 (푔ℎ) 푡

3-67 3-68 Pelton Wheel Francis and Kaplan Turbines

http://www.photobucket.com

휔 휔

Adjustable Adjustable guide 휔 Rotor guide Rotor blades vanes vanes 휔

Typical bucket design Draft tube

• Compare Pelton, Kaplan and Francis turbines: https://www.youtube.com/watch?v=k0BLOKEZ3KU Francis turbine 3-69 (radial flow) (axial flow) 3-70

Francis and Kaplan Turbines (cont’d) Turbines (cont’d)

Exercise: A Francis turbine is being designed for a hydroelectric dam. Instead of starting from scratch, the engineers decide to geometrically scale up a previously Runner of a Kaplan turbine designed turbine that has an excellent performance history. The existing turbine (turbine A) has diameter 퐷퐴 = 2.05 m, and spins at 푁퐴 = 120 rpm. At its best efficiency 3 point, 푄퐴 = 350 m /s, ℎ퐴 =75 m 풫푡 = 242 MW. The new turbine (turbine B) is for a larger facility. Its generator will spin at the same speed (120 rpm), but its net head will be higher (ℎ퐵 = 104 m).

a) Calculate the diameter (퐷퐵) of the new turbine such that it operates most efficiently, and calculate 푄퐵, and 휂퐵. www.tbhic.cn Runner of a Francis turbine b) Calculate the turbine specific speeds of both turbines.

www.geppert.at

• Francis turbine: https://www.youtube.com/watch?v=3BCiFeykRzo https://www.youtube.com/watch?v=IZdiWBEzISM

• Kaplan turbine: https://www.youtube.com/watch?v=0p03UTgpnDU https://www.youtube.com/watch?v=_eLufvzh5HU 3-71 3-72 Turbines (cont’d)

Exercise : Calculate the specific speeds of the following turbines a) Francis type radial flow turbine at the Round Butte hydroelectric power station in Madras rotating at 180 rpm and producing 119 MW of power at a flow rate of 127 m3/s from a head of 105 m. b) Francis type mixed flow turbine at the Smith Mountain hydroelectric power station in Roanoke, VA, rotating at 100 rpm and producing 194 MW of power at a flow rate of 375 m3/s from a head of 54.9 m. c) Kaplan type axial flow turbine at the Warwick hydroelectric power station in Cordele, GA, rotating at 100 rpm and producing 5.37 MW of power at a flow rate of 63.7 m3/s from a head of 9.75 m.

Exercise : Learn the meaning of the following turbine related terms Runner blade, wicket gate, stay vane, crown, penstock, draft tube, tail water

Exercise : How does hydraulic power work? http://www.youtube.com/watch?v=cEL7yc8R42k

Virtual turbines http://www.youtube.com/watch?v=HzQPNpP55xQ 3-73