11 - hydraulic machinery

Hydraulic Machinery

Chapter 14: Turbomachinery ME33 : Fluid Flow 2

Objectives

Identify various types of pumps and turbines, and understand how they work

Apply dimensional analysis to design new pumps or turbines that are geometrically similar to existing pumps or turbines

Perform basic vector analysis of the flow into and out of pumps and turbines

Use specific speed for preliminary design and selection of pumps and turbines

Hydraulic Machinery Herrera, Eugene C.

Water Resources Engineering II


Pump: adds energy to

a fluid, resulting in an

increase in pressure

across the pump.

Turbine: extracts

energy from the fluid,

resulting in a

decrease in pressure

across the turbine.

Hydraulic Machinery Two-types




Hydroelectric Generation

Three Basic Elements for

Power Generation

Draft tubes convey water from the discharge side of the turbine to the

tailrace.

Tailrace maintains a minimum tailwater elevation below the power plant and

keeps the draft tube submerged.

Physical Elements

A means to create Head

- dam and reservoir

- intake structures

Conduit to Convey Water

- intake structures

- penstocks

Power Plant

- turbines/generators

- draft tubes

- tailrace




Hydroelectric Generation Energy Elements

For a constant discharge, the energy relation between the forebay and any

other section is,

Forebay is a regulating reservoir that temporarily stores water to facilitate:

1) low-approach velocity to intake, 2) surge reduction, 3) sediment removal,

or 4) storage.

2 2

1 1 2 2/ 2 / 2 cz V g z V g h




Turbines Two basic types

Impulse-turbine, a free jet of water impinges on the revolving element of the

machine, which is exposed to atmospheric pressure. Kinetic to mechanical energy.

Reaction turbine, flow takes place under pressure in a closed chamber. Kinetic

and pressure head to mechanical energy.

Impulse-turbine Reaction-turbine




Turbines Impulse-types

The impulse turbine is also called a tangential waterwheel or a Pelton wheel has

a runner with numerous spoon-shaped buckets attached to the periphery and are

driven by one or more jets of water issuing from fixed or adjustable nozzles.

Working heads can range between 30 to 300 meters.

Jet on bucket is split into 2 parts that

discharge at sides of the bucket

One jet for small turbines, many for big

Wheel speed is kept constant under

varying load through a governor

Bypass valves or deflectors are provided

to prevent water hammer

Can be double overhung

Provided with housing to prevent

splashing

For efficiency: bucket width is 3-4x jet

diameter and 15-20x for wheel diameter

Bucket angle is usually 165o.




Turbines Reaction-types

Reaction turbines include Francis turbines, which are constructed so that water

enters the runner radially and then flows towards the center and along a turbine

shaft axis. Working heads can range between 30 to 450 meters and most

economical for 45-450 meters.

Jet enters a scroll case, moves in to the

runner through a series of guide vanes

Vanes convert pressure head to velocity head

Vanes are controllable for regulating flows

Relief valves/surge tanks are provided to

prevent water hammer

Usually mounted on a vertical axis

From the runner, water enters a draft tube

with a gradually increasing cross-sectional

area to reduce discharge velocity.

To prevent flow separation, the divergence

angle should be less than 10o.

To prevent cavitation, z1 should be limited.




Turbines Other types

Fixed-blade propeller turbines are constructed so that water passes through the

propeller blades in an axial direction. Adjustable gates upstream are used to

regulate flow. These turbines are typically used in the 3-60 meter head range and

are economical for 15-45 meters.

Kaplan turbines are propeller turbines with adjustable pitch blades that operate in

the same range of heads. The usual runner has 4-8 blades mounted on a hub, with

very little clearance between the blades and the conduit wall. Adjustable gates

upstream of the runner regulate the flow.




Turbines Other types

Tubular turbines have a guide vane assembly that is in line with the turbine and

contributes to the tubular shape. Economical choice for heads less than 15 meters.

Bulb turbines are horizontal axial-flow turbines with a turbine runner directly

connected to a generator or through a speed-increasing gear box. A rim turbine is

similar to the bulb turbine with the generator mounted on the periphery of the

turbine runner blades. Economical choice for heads less than 15 meters.




Turbines Types and heads




Turbines Hydraulics of Impulse-types

The impulse turbine rotates at a velocity u at the center line of the buckets. When

the water enters the bucket, it is in position A and the bucket moves to position B,

where the water leaves the bucket. The velocity changes from V1 at the entrance

to V2 at the exit.

The velocity v represents the velocity of the water relative to the bucket. So that at

entry,

Ignoring fluid friction, the magnitude of v remains constant with a change in

direction, so that it is tangential to the bucket.

1V u




Turbines Hydraulics of Impulse-types

The force exerted by the water on the bucket is given by,

In terms of relative velocity,

1( cos ) ( )(1 cos )F Q Q V u

1 2( cos )F Q V V

The power transmitted to the bucket is the product of force and velocity,

1V u

1( )(1 cos )P Fu Q V u u

No power is developed when u = 0 or u = V1. Maximum power with respect to u

occurs when,

1/ (1 cos )( ) 0dP du Q V u u

Which can be solved for . This means that, when friction is negligible, the

best hydraulic efficiency occurs when the peripheral speed of the wheel is half of

the velocity of the jet of water.

1 / 2u V

The break power delivered by a turbine to the generator is,

550

ep

hBh Q

w eBk Qh; English units ; SI units Bhp is in horsepower

Bkw is in kilowatts

he is the effective head




Turbines Hydraulics of Reaction-types

The velocity is at the entrance edge of the runner blade, where is the

rotative speed of the runner in radians per second. This entering velocity to the

blade is essentially tangential to the exit end of the guide vane.

1 1u r

The component of V1 that is

tangent (VT1) to the entrance of the

runner blade is,

1 1 1 1cott rV r V

The tangential component of the

velocity at the exit is,

2 2 2 2cott rV r V

The torque T exerted on the

runner blades is,

1 1 2 2( )t tT Q V r V r

The power transmitted to the

turbine from the water is,

1 1 2 2( )t tP T Q V r V r





The following continuity equation can be used to determine the radial velocity

components,

1 1 2 22 2r rQ rZV r ZV

As with pumps, the concept of a turbine-specific speed is defined. For turbines, we

are more interested in the power of the turbine than the discharge. The

dimensional form of the specific speed ns used by the hydraulic turbine industry is,

1/2

5/4s

NPn

H

rotational speed in rpm

power in horsepower (kilowatts)

head in turbine in feet (meters)

N

P

H

Cavitation in turbines is very undesirable, since it causes pitting, mechanical

vibration, and loss of efficiency. Cavitation can be avoided by designing, installing,

and operating turbines so that the local absolute pressure never drops to the vapor

pressure of the water. The susceptibility to cavitation in turbines is given by the

cavitation index,

1 0/ / ( )o vp p z z

H

1

0

absolute atmospheric pressure

absolute vapor pressure of water

elevation of D/S side of turbine

elevation of tailrace water

net head across the turbine

o

v

p

p

z

z

H

h m v

overall efficiency

hydraulic efficiency

mechanical efficiency

volumetric efficiency

h

m

v

1 0 / /o v cz z p p H





For a given turbine operating with a given H and speed, if z1 is increased or p0

decreased, the pressure acting on the blades of the turbine decreases and

eventually reaches a point at which cavitation would occur. Then lower values of

σ indicate a greater tendency for cavitation. Cavitation susceptibility also changes

with the speed of the impeller because greater speed means greater relative

velocities and less pressure on the downstream side of the impeller. Critical σc

values are obtained from experiments.

Turbine Efficiency

Curves




Turbines Turbine Law

If the peripheral speed of a turbine is expressed as , then:

1 2u gh

1 1

1/2 1/2 1/2

2 / 60 / 2

2 2 2

N Du r

gh gh gh

1/2

153.3

DN

h

1/2

84.6

DN

h ; English units ; SI units

nominal diameter of the runner

rotative speed in revolutions per minute

total effective head

D

N

h

For any turbine, there is a value of that gives the highest efficiency. Designating

this as , its magnitude for the various turbine types is about

e

Impulse wheel: 0.43-0.48

Francis turbine: 0.60-0.90

Propeller turbine: 1.4-2.0

N should be constant for turbines

Φ is a function of h and Φ cannot be constant for

varying h values resulting to efficiency drop

Gate opening changes to vary with Q will maintain constant rotative speed

Change in gate opening changes velocity vectors at runner entrance and exit

Water will no longer enter blade tangentially, increasing headloss in runner,

lower efficiency




Turbines Turbine Law

Two turbines of identical geometric shape but of different size will have the same

specific speed.

1/2

5/4s

NPn

H

The relative sizes of any two turbines is determined from,

1 1 1

2 2 2

D N

D N

More power is developed by a reaction wheel of a given diameter than by an

impulse wheel of the same size and operating under the same head.

The trend of hydraulic turbine design is toward higher specific speed, leading to

smaller and higher-speed machines for the same design requirements and output.

Two turbines of identical geometric shape but of differing size will have practically

the same efficiency if operated so that their Φ values are the same, since the

velocity diagrams will be proportional.




Turbines Sample Problem

PROBLEM. A turbine is to be selected for an installation where the net head is 600 ft

and the permissible flow is 200 cfs. What type of turbine should be chosen if the

desired operating speed is 100 rpm?.

SOLUTION. Assuming 90 percent efficiency, the available power is,

62.4 200 600 0.912,300

550 550

Qh x x xhp

Given an operating speed of 100 rpm,

1/2

5/4

100(12,300)3.7

600s

This indicates that an impulse wheel should be selected. This turbine will not be

subject to cavitation for the given operating conditions.

The required wheel diameter (assuming φ = 0.45) is found to be,

1/2153.3(600) 0.4516.9

100

xD ft

A wheel diameter of 16.9 ft would be quite large, and a small size could be selected by

increasing the rotative speed.

Hydraulic Machinery

Herrera, Eugene C.



Positive-displacement machines (reciprocating or rotary)

Closed volume is used

to squeeze or suck fluid.

Pump: human heart

Dynamic machines No closed volume. Instead, rotating blades supply or extract energy.

Enclosed/Ducted Pumps: torpedo propulsor

Open Pumps: propeller or helicopter rotor

Pumps Major Categories




Pumps

For gases, pumps are further broken down into

Major Categories

Fans: Low pressure gradient, High volume flow rate. Examples include ceiling fans and propellers.

Blower: Medium pressure gradient, Medium volume flow rate. Examples include centrifugal and squirrel-cage blowers found in furnaces, leaf blowers, and hair dryers.

Compressor: High pressure gradient, Low volume flow rate. Examples include air compressors for air tools, refrigerant compressors for refrigerators and air conditioners.




Dynamic Pumps

Dynamic Pumps include

centrifugal pumps: fluid enters

axially, and is discharged

radially.

mixed--flow pumps: fluid enters

axially, and leaves at an angle

between radially and axially.

axial pumps: fluid enters and

leaves axially.

Types




Centrifugal Pumps

Snail--shaped scroll

Most common type of pump:

homes, autos, industry.

Low cost, simple and reliable in a

wider range of flows and heads

Pump capacity (Q) is the flow

rate or discharge of a pump

Head is the difference in

elevation between a free surface

of water above (or below) a

reference datum (varies with

pump type).

Any pump in which fluid is energized by a rotating impeller, whether the

flow is radial, axial, or a combination of both (mixed). Has 3 types (radial,

axial and mixed flow)

Description




Centrifugal Pumps Description

Typical flow paths in

centrifugal pumps. (a)

radial vertical; (b)

mixed; (c) radial

horizontal; (d) axial





Multistage pumps are pumps with more than one impeller (stage). The

stages are in series. The impellers are on a single shaft and are enclosed

in a single pump housing.

Single and multistage pumps





Illustration of total dynamic

head and net positive

suction head




Centrifugal Pumps: Blade Design

Side view of impeller blade. Vector analysis of leading

and trailing edges.

Hydraulics




Centrifugal Pumps: Blade Design

Blade number affects efficiency and introduces circulatory

losses (too few blades) and passage losses (too many blades)

Hydraulics




Centrifugal Pumps Operating characteristics

Operating characteristics of pumps are dependent upon their size, speed,

and design. For centrifugal pumps, similar flow patterns occur in

geometrically similar pumps. From dimensional analysis:

3Discharge coefficient: Q

QC

nD

2 2 2 2Head coefficient: ;H

H gHC

n D n D

3 5Power coefficient: P

PC

n D

3 3

2 2

pump capacity in m /s (ft /min)

speed in radians per second (rpm)

impeller diameter in meters (ft)

head in meters (ft)

acceleration due to gravity in m/s (ft/s )

power input in kilowatts

Q

n

D

H

g

P

3

(hp)

density in kg/m (slugs per cubic foot)

Affinity laws are defined for a pump operating at two different speeds with

the same diameter:

1 11 2

2 2

:Q n

CQ CQQ n

2

1 11 2

2 2

:H n

CH CHH n

3

1 11 2

2 2

:P n

CP CPP n




Reynolds number also appears with a relationship, but in terms of angular rotation

Reynolds number

Functional relation is

Head coefficient

Power coefficient

Centrifugal Pumps Dimensional Analysis




Centrifugal Pumps Sample Problem: Affinity Law

Problem (Mays, 12.2.1). A pump operating at 1800 rpm delivers 180

gal/min at 80 ft head. If the pump is operated at 2160 rpm, what are the

corresponding head and discharge?

Solution. Use the affinity law to compute for the corresponding

requirements.

2160

1800

2160

2

2160

1800

2

2160

2160

1800

2160180 216 / min

1800

2160

1800

216080 115.2

1800

Q

Q

Q gal

H

H

H ft




If two pumps are

geometrically similar, and

The independent ’s are

similar, i.e.,

CQ,A = CQ,B

ReA = ReB

A/DA = B/DB

Then the dependent ’s

will be the same

CH,A = CH,B

CP,A = CP,B

Centrifugal Pumps Operating characteristics




Centrifugal Pumps Specific Speed

The specific speed ns is a parameter used to select the type of centrifugal

pump that is best suited to a particular application.

1/231/2 1/2

3/43/4 3/42 2

/

/

Q

s

H

Q nDC nQn

C HH n D

The total dynamic head is the head against which a pump must operate.

For a given speed of pump operation, the Q and H must be at the point of

maximum efficiency.

For dimensional correctness, use a conversion factor of 17, 200.

In determining the specific speed of multistage pumps, the head is the

head per stage. Because ns is related to 1/H3/4, ns decreases with an

increase in H and the efficiency is small for the smaller ns, one impeller

used for large heads results in low efficiency. Multistage pumps can

increase efficiency.

Hydraulic Machinery

Herrera, Eugene C.



Centrifugal Pumps Specific Speed

Pump efficiency as related

to specific speed and

discharge




Centrifugal Pumps Sample Problem: Specific speed

Problem (Mays, 12.2.2). A flow of 0.02 m3/s must be pumped against a

head of 25 m. The pump will be driven by an electric motor with a speed of

1450 rpm. What type of pump should be used and what is the

corresponding efficiency?

Solution. Compute the specific speed,

1/2 1/2

3/4 3/4

1450(0.02)18.34

(25)s

nQn

H

From the figure of specific speed vs. efficiency, we find that a radial flow

centrifugal pump would be used with an efficiency of around 68%.




Centrifugal Pumps Cavitation and Net Positive Suction Head

Cavitation occurs in pumps when the absolute pressure at the pump inlet

decreases below the vapor pressure of the fluid, at which time vapor

bubbles form at the impeller inlet (suction side).

The bubbles are transported through the impeller, where they reach a

higher pressure and abruptly collapse. Collapse of the bubbles produces

noise and vibration.

Hydraulic Machinery

Herrera, Eugene C.




The available net positive suction head (NPSHA) at the eye of the

impeller is computed and compared to the required net positive

suction head (NPSHR) of the pump, specified by the manufacturer.

The available net positive suction head (NPSHA) is the absolute

dynamic head in the impeller eye, defined by.

ent f m

atm vA s L L L

p pNPSH Z h h h

atmospheric pressure head in meters (feet)

static suction head in meters (feet)

vapor pressure head in meters (feet)

entrance headloss in meters (feet)ent

atm

s

v

L

p

Z

p

h

suction pipe friction headloss in meters (feet)

sum of minor losses of valves and fittings in meters (feet)m

Lf

L

h

h

The NPSHA should always be greater than the NPSHR.

Thoma’s cavitation constant is defined as the ratio of net positive

suction head at the point of cavitation inception (NPSHi) to the total

dynamic head H.

iNPSH

H





When applied to multistage pumps, H is the dynamic total head per stage.

Thoma’s cavitation constant can be related approximately to specific

speed and pump efficiency.

4/3

610

sKn

Thoma’s cavitation constant should not be used for design decisions,

instead recommended values of NPSHR.

4/3

610

si

HKnNPSH




Pump Cavitation and NPSH

Cavitation should be avoided due

to erosion damage and noise.

Cavitation occurs when P < Pv

Net positive suction head

NPSHrequired curves are created

through systematic testing over a

range of flow rates V.

Cavitation and Net Positive Suction Head




Centrifugal Pumps Sample Problem

Problem (Mays, 12.2.4). Estimate the available net positive suction head

(NPSHA) for a new system with the configuration shown below for a

discharge of 0.12 m3/s. The suction piping and the discharge piping are

both cement mortar-lined ductile iron pipe with a Hazen-Williams

coefficient of 140. The suction piping has an inside diameter of 300 mm

and a length of 5 m. The static suction head is +3m.The system has a

bellmouth entrance, two 90o bends, and a gate value on the suction side.

The elevation is at 1000 m above mean sea level, the temperature is 200C

and patm /γ=9.19 m.

Solution. The NPSHA is computed

using:

ent f m

atm vA s L L L

p pNPSH Z h h h





Referring to tables for vapor pressure head of water at 20oC, pv/γ = 0.25

m. The losses due to friction are computed using the Hazen-Williams

equation:

0.63 0.540.849 fV CR S

1.85 1.85

4.87

2.63

15110,700Lf

Q Qh D

C CD

The friction loss in meters per 1000 m of pipe length can be expressed

more conveniently from:

1.85

4.870.1210,700 (0.300)

140

7.988 m per 1000 m of pipe

7.988 (5 m/1000 m) = 0.0399 m total loss

Lfh

Bend losses (suction piping):

0.121.69 /

0.0706

QV m s

A

2

2Lb

Vh K

g





Gate valve loss (suction piping):

0.121.69 /

0.0706

QV m s

A

2(1.69)0.2 0.029

2(9.81)GLh m

Bellmouth entrance loss:

0.05K 2

1

(1.69)0.05 0.007

2(9.81)Lenth m

Total minor losses:

0.036 0.036 0.029 0.007 0.108mLh m

ent f m

atm vA s L L L

p pNPSH Z h h h

Solving for NPSHA:

9.19 3 0.25 0.0399 0.108 11.79ANPSH




Centrifugal Pumps Pump Characteristics

A pump head-characteristic curve is a graphical representation of the total

dynamic head versus the discharge that a pump can supply.

Manufacturer’s

pump

performance

curves





When two or more pumps are operated, the pump station losses, which

are the headlosses associated with the piping into and out of the pump,

should subtracted from the manufacturer’s pump curves to derive a

modified head characteristic curves.

Modified pump

performance

curves





Shutoff head is the head output by the pump at zero discharge. Normal

discharge (head) or rated capacity is the discharge (or head) where the

pump is operating at its most efficient level. There is a set of pump curves

for a single pump. System operation depends on flow requirements.

Pump performance

curves for variable

speed pumps





Pumps in series or parallel requires the addition of modified head-

characteristics curves. For pumps in parallel, curves are added

horizontally with the respective heads the same. For pumps in series,

curves are added vertically with the respective discharges the same.

Pumps in parallel Pumps in series





Pump manufacturers also provide curves relating brake horsepower

(required by the pump) to the pump discharge.

:550

QHbhp English

e

: SI

QHbhp

e

3

3 3

brake horsepower in hp (kilowatts)

pump discharge in cfs (m /s)

total dynamic head in ft (m)

specific weight of water in lb/ft (KN/m )

pump efficiency

bhp

Q

H

e

Pump efficiency is the power delivered by the pump to the water (water

horsepower) divided by the power delivered to the pump by the motor

(brake horsepower)

Pumps operate best at their best efficiency point (bep) because of

minimum radial loads on the impeller and minimum cavitation problems.





Operating ranges of a pump can be developed by (1) establishing a

minimum acceptable efficiency and (2) setting upper and lower limits on

the allowable impeller diameters.




Matching a Pump to a Piping System

Steady operating

point:

Energy equation:

Design



11 - hydraulic machinery

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