Centrifugal Machine

7/30/2019 Centrifugal Machine

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Expression relating Q, H, P

developed by Rotary machines

Rotary Machines include:

Centrifugal (or radial),

Axial, andMixed types

In such machines when fluid passes throughblade passage static pressure changes.


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Axial flowMixed flow

Centrifugal (Unit # 2)


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CENTRIFUGAL MACHINE

12.2.1


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A typical radial flow pump.


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We already know from Mechanics

1. For a rotary machine

Power = Angular velocity x Torque= Mass flow rate x Head

Torque = Rate of change of angularmomentum= Mass x [Abs. Circum. velocity x radius

(in-out)] T = [Q] (r2Vt2 r1Vt1)


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Idealized radial-flow impeller

(a) impeller; (b) velocity diagrams.


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Relative Velocity

(Fluid entering periphery)


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P


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Power(In terms of flow rate & Blade angle)

From velocity triangle:Vt= Vncot= u Vncot

where Vn is radial component ofV

From aboveP=Q(u2Vt2 u1Vt1)

= Q(u2Vn2 cot u1Vn1 cot ) (5)

NOTE

1. To minimize entrance lossBlade angle is equal to the entry angle of fluid to the blade.

2. To minimize exit lossFluid entry angle () is equal to the angle of the guide vane

=Angle between tip and absolute velocity =Angle between tip and relative velocity


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Symbols to be used

Velocities:V- Absolute fluid velocityv - Relative fluid velocity

u - peripheral speed of blade Subscripts:

1 - inlet

2 - outletn - normal component

t- tangential component

Geometry:b - blade widthr- blade radius

- angle between Vand u vectors- angle between v and u vectors


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Head

Power,P= Weight flow rate x Head = P = (Qg) H Head of fluid column,

H = P/(Q .g)] (6)

Substituting P from Eq.5 we get(7)

For highest head cot 1 = 0; i.e 1 = 90 (8)

Substituting:Flow rate, Q = Vn.2r b; Tip velocity u2= wr2, we canget

(9)

( )g

VuVu

g

VuVuH nntt

)cotcot( 1112221122 =

=

( )g

Vuu

g

VuH nt

)cot( 222222 ==

Qgbg

rH 22

2

2

2cot

=2


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Summary of what we have learnt

From geometryVn

2 = V2-Vt2 = v2- (u Vt)

2

u Vt= (V2+ u2v2)/2 (12)

where u = velocity of blade,V

t= tangential component of absolute velocity of fluid

From (4) & (12) (13)

Head = Kinetic energy gain + Pressure rise

g

VVuu

g

VV

H

g

VuVVuV

Qg

PH

rr

rr

2

)()(

2

)(

2

1

2

2

2

1

2

2

2

1

2

2

21

21

21

22

22

22

+

=

++==


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SUMMARYSUMMARY

Blade angle () is ideally the angle between therelative velocity (V

r) and blade-tip velocity (u)

vectors To draw the vector diagram note that the blade-tip

velocity and relative velocity vector are in the

same rotational (clockwise or anticlockwise)direction. Third side of the triangle is the absolutevelocity vector which is in opposite direction.

Power = [blade velocity x tangential component ofabsolute velocity] inlet outlet

Flow ~ Rotor circumference x width x Normalvelocity


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What we have learnt

Blade angle () is ideally the angle between the relativevelocity (Vr) and blade-tip velocity (u) vectors

To draw the vector diagram note that the blade-tip velocityand relative velocity vector are in the same rotational

(clockwise or anticlockwise) direction. The arm of the

triangle is the absolute velocity vector which is in oppositedirection.

Power = [blade velocity x tangential component of absolute

velocity] inlet outlet

Flow ~ Rotor circumference x width x Normal velocity

Blade shapes


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Blade shapes

Straight (radial) blade wheel

Forward curve wheel

Backward curve wheel


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Vector diagram of a centrifugal

pump/fan

FLOW CHARACTERISTICS


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FLOW CHARACTERISTICS

Head = Power delivered to fluidFluid flow rate (weight)H=Pw /( Q g) = (u2Vt2 u1Vt1 g

For maximum head, Vt1u2Vt2/g

From velocity diagram, Vt2= u2-Vn2cot2 Flow rate discharge, Q = 2 r2 bVn2 So,H = [u2

2-(Q/2 r2 b) u2cot2]/g = A B.Q cot2


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Efficiency

Ideal Head varies linearly with discharge (Q).

Head (H) increases or decreases with Q

depending on blade angle2

With valve shut off . i.e Q = 0

For pumps/fans:

Efficiency =

wherePis the power consumedPQgH=

guH

2

2=


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Ideal H vs Q characteristics


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Effect of blade configuration on

Performance Depending upon the value of exit blade angle the

head increases or decreases with increase in flow

Energy transfer ~ Vt2. From velocity diagram, fora given tip velocity, u forward & radial curve

blades transfer more energy

Backward blades give higher efficiency

Forward and radial are smaller in size for the sameduty, but have lower efficiency

Centrifugal compressor uses radial blades for

better strength against high speed rotation


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Characteristics of different types

of blades Owing to the losses the

actual characteristic isdifferent from

theoretical linear shape

Power consumptionvaries with flow Q

Efficiency varies with

Q with highest valuebeing in the design

condition


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Home work

1. Show that the manometric head for apump having a discharge Q and running at

a speedNcan be expressed by an equation

of the formHm=AN2+BNQ+CQ2, whereA,B,Care constants.

Example


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Example

1. A centrifugal pump impeller is 255 mm diameter, thewater passage 32 mm wide at exit, and the vane angle atexit 30. The effective flow area is reduced by 10%

because of vane thickness. The manometric efficiency is80% when the pump runs at 1000 rpm and delivers 50litre/s.

Calculate the manometer head measured between inletand outlet flange of the pump assuming 47% of thedischarge head is not converted into pressure head.

Assume the pump delivers maximum head.

Centrifugal Machine

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