Characteristics of Centrifugal Fan/Pumppoisson.me.dal.ca/site2/courses/mech3300/TURBOM_2.pdf ·...
Transcript of Characteristics of Centrifugal Fan/Pumppoisson.me.dal.ca/site2/courses/mech3300/TURBOM_2.pdf ·...
Theory of turbo machineEffect of Blade Configuration on
Characteristics of Centrifugal machines
Unit 2(Potters & Wiggert Sec. 12.2.1, &-607)
Expression relating Q, H, Pdeveloped by Rotary machines
• Rotary Machines include: Centrifugal (or radial),Axial, andMixed types
• In such machines when fluid passes through blade passage static pressure changes.
• Axial flowMixed flow →→
Centrifugal (Unit # 2)• ↓
<— Axial flow (Unit #4)
CENTRIFUGAL MACHINE
12.2.1
A typical radial flow pump.
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 angular
momentum= Mass x [Abs. Circum. velocity x radius (in-out)]
T = [ρ Q] (r2Vt2 – r1Vt1)
Idealized radial-flow impeller (a) impeller; (b) velocity diagrams.
Relative Velocity(Fluid entering periphery)
Power (In terms of flow rate & Blade angle)
• From velocity triangle:Vt= Vncotα = u – Vncotβ
where Vn is radial component of V• From above
P = ρ Q(u2Vt2 – u1Vt1) = ρ Q(u2Vn2 cotα2 – u1Vn1 cotα1 ) (5)
• NOTE1. To minimize entrance loss
Blade angle β is equal to the entry angle of fluid to the blade.2. To minimize exit loss
Fluid entry angle (α) is equal to the angle of the guide vane3. α = Angle between tip and absolute velocity
β = Angle between tip and relative velocity
Symbols to be used• Velocities:
V - Absolute fluid velocityv - Relative fluid velocityu - peripheral speed of blade
• Subscripts:1 - inlet
2 - outletn - normal component
t - tangential component• Geometry:
b - blade widthr - blade radiusα - angle between V and u vectorsβ - angle between v and u vectors
Head• Power, P = Weight flow rate x Head = P = (ρ Qg) H• Head of fluid column,
H = P/(ρ Q .g)] (6)Substituting P from Eq.5 we get
(7)
• For highest head cot α1 = 0; i.e α1 = 90– (8)
• Substituting:Flow rate, Q = Vn.2π r b; Tip velocity u2= wr2 , we can
get– (9)
( )g
VuVug
VuVuH nntt )cotcot( 1112221122 αα −=
−=
( )g
VuugVuH nt )cot( 222222 β−
==
Qgbg
rH 22
22
2cotπ
βωω−=
2
Summary of what we have learnt • From geometry
Vn2 = V2-Vt
2 = v2- (u –Vt )2
u Vt = (V2+ u2 –v2)/2 (12)where u = velocity of blade,
Vt= tangential component of absolute velocity of fluid
• From (4) & (12) (13)
•
• Head = Kinetic energy gain + Pressure rise
gVVuu
gVVH
gVuVVuV
QgPH
rr
rr
2)()(
2
)(
21
22
21
22
21
22
21
21
21
22
22
22
−−−+
−=
−+−−+==
ρ
SUMMARYSUMMARY
• Blade angle (β) is ideally the angle between the relative velocity (Vr) 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 absolute velocity vector which is in opposite direction.
• Power = [blade velocity x tangential component of absolute velocity] inlet – outlet
• Flow ~ Rotor circumference x width x Normal velocity
What we have learnt• Blade angle (β) is ideally the angle between the relative
velocity (Vr) 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. The arm of the triangle is the absolute velocity vector which is in opposite direction.
• Power = [blade velocity x tangential component of absolute velocity] inlet – outlet
• Flow ~ Rotor circumference x width x Normal velocity
Blade shapes• Straight (radial) blade wheel
• Forward curve wheel• Backward curve wheel
Vector diagram of a centrifugal pump/fan
FLOW CHARACTERISTICS• Head = Power delivered to fluid
Fluid flow rate (weight) H = Pw /(ρQ g) = (u2Vt2 – u1Vt1 )/g
• For maximum head, Vt1 = 0Η = u2Vt2 /g
• From velocity diagram, Vt2= u2-Vn2cotβ2 • Flow rate discharge, Q = 2 πr2 bVn2• So, H = [u2
2-(Q/ 2 πr2 b) u2cotβ2]/g• = A – B.Q cotβ2
Efficiency
• Ideal Head varies linearly with discharge (Q). • Head (H) increases or decreases with Q
depending on blade angle β2
• With valve shut off . i.e Q = 0
• For pumps/fans: • Efficiency =
where P is the power consumed PQgHρη =
gu
H22=
Ideal H vs Q characteristics
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, for a 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 same
duty, but have lower efficiency• Centrifugal compressor uses radial blades for
better strength against high speed rotation
Characteristics of different types of blades
• Owing to the losses the actual characteristic is different from theoretical linear shape
• Power consumption varies with flow Q
• Efficiency varies with Q with highest value being in the design condition
Home work
1. Show that the manometric head for a pump having a discharge Q and running at a speed N can be expressed by an equation of the form Hm=AN2+BNQ+CQ2, where A,B,C are constants.
Example1. A centrifugal pump impeller is 255 mm diameter, the
water passage 32 mm wide at exit, and the vane angle at exit 30. The effective flow area is reduced by 10% because of vane thickness. The manometric efficiency is 80% when the pump runs at 1000 rpm and delivers 50 litre/s. Calculate the manometer head measured between inlet and outlet flange of the pump assuming 47% of the discharge head is not converted into pressure head. Assume the pump delivers maximum head.