Transcript Slide 1

ENERGY CONVERSION
MME 9617A
Eric Savory
www.eng.uwo.ca/people/esavory/mme9617a.htm
Lecture 9 – Prime movers and
turbomachinery
Department of Mechanical and Material Engineering
University of Western Ontario
Definition
• Turbomachinery describes machines that
transfer energy between a rotor and a fluid,
including both turbines and compressors.
• A turbine transfers energy from a fluid to a rotor,
a compressor transfers energy from a rotor to a
fluid.
• The two types of machines are governed by the
same basic relationships including Newton's
second law of motion and Euler's energy
equation.
• Centrifugal pumps are also turbomachines that
transfer energy from a rotor to a fluid, usually a
liquid.
• Energy is converted from kinetic to potential and
vice versa with the ‘aid’ of mechanical energy.
Pump classes and types
Class
Centrifugal (rotating
impeller; increases the
pressure energy of a fluid)
Type
Volute
Diffuser
Regenerative turbine
Mixed flow
Axial flow
Rotary (positive
Gear
displacement pump;
Vane
produces the same volume Cam and piston
output regardless of
Screw
pressure)
Lobe
Reciprocating (pistons or
plungers displace the
fluid)
Direct acting
Diaphragm
Rotary piston
Positive displacement pumps:
Reciprocating
piston
Double
screw
pump
Three-lobe
pump (left)
Double
circumferential
piston (centre)
External
gear pump
Sliding
vane
Flexible
tube
squeegee
(peristaltic)
Pump types
Centrifugal pump cutaway schematic
Formulation of the concept
• We will focus on the ‘centrifugal pump’. However, the
principles are the same for compressors and turbines
with a geometry change and appropriate boundary
conditions.
• The dominant direction of the flow during the energy
transfer process is radial.
• Rotor (impeller) – rotating element where the energy
transfer process occurs.
• Diffuser – stationary element which is responsible for the
transformation of the velocity head into static pressure.
• Velocity head - V2/2g
Centrifugal pump
with volute and diffuser
Energy transfer mechanism
• The energy transfer mechanism results from the change
in angular momentum of the fluid:


V
 M  t CV  r  V  g dVol  CS  r V  g dA
• The torque on the shaft is:
   rVu
CV
V
g
dA
• Where Vu denotes the component of the vector V in the
direction of U, the tangential wheel speed (at a given
U=rw), assuming steady-state frictionless flow.
• Further assumptions of uniform flow at the inlet and outlet
and an ‘effective’ mean radius, give:
m
   r2Vu 2  rV
1 u1 
g
• Power becomes:
P  w 
m  r2wVu 2  r1wVu1 
g

m U 2Vu 2  U1Vu1 
g
• The increase in Head is
(Euler pump equation):
P U 2Vu 2  U1Vu1
H 
m
g
• U2Vu2 > U1Vu1 – the device functions as a
compressor
• U2Vu2 < U1Vu1 – energy is extracted from the
flow and the device function as a turbine
The velocity triangle
• V - absolute velocity
• U - tangential velocity
• Vr - relative velocity
V  U  Vr
Centrifugalcompressor
schematic
and
velocity
triangles
• From figure (a) in previous slide, fluid enters the rotor with
an absolute velocity that is completely radial (‘zero preswirl’), therefore, Vu1 is zero. The increase in Head is:
U 2Vu 2
H
g
• Denoting the radial component of the exit velocity as Vm,
then:
V
cot 2 
ru 2
Vm
Vu 2  U 2  Vru 2  U 2  Vm cot 2
• And from the exit velocity
triangle fig. (c):
U 2  U 2Vm cot  2
2
H
g
• For an impeller of width w, the volume flow rate is:
Q   D2 wVm
Head (H) versus Volume flow rate (Q)
relationships
• The increase in Head is a function of the volumetric flow
rate, Q:
2
U2
U2
H

Q cot  2
g
• Defining:
2
U
K1 
,
g
 Dwg
2
U
K2 
cot 2
 Dwg
• We obtain:
H  K1  K 2Q
• The sign on K2 (which depends on the exit angle 2)
establishes the characteristics of the machine
H - Q characteristics
Three separate cases can be considered:
(1) Radial exit blades (2 = 90o)
(2) Backward-curved blades (2 < 90o)
(3) Forward-curved blades (2 > 90o)
“Ideal” H versus Q curves
Actual H - Q relationships
Losses inside pump (e.g. friction
and turning losses)
Head
H
Volume flow rate Q
Manufacturer’s pump characteristics
Index of pumps
from
Goulds Pumps
Inc
The
“Goulds 3196”
family of
pumps
Composite rating
charts for the
“Goulds 3196”
family of pumps
Performance characteristics
Symbol
Parameter
Imperial Units
H
Head (m)
ft-lbf/lbm
Q
Flow rate (m3/s)
ft3/s
N
Speed (rpm or rad/s)
rpm
η
Mechanical efficiency
none
D
Geometry (m)
ft
ρ
Density (kg/m3)
lbm/ft3

Viscosity (kg/ms)
lbm/ft-s
P
Power (W)
ft-lbf/s
Buckingham P theory
A dimensional analysis of all
the variables involved yields a
number of non-dimensional
groups called  parameters:
Note that although the
viscosity  is an appropriate
parameter to include and it
yields the Reynolds number
(4), in practice this is not a
dominant parameter for
turbomachine scaling analysis
Q
1 
3
ND
H
2  2 2
N D
P
3 
3 5
N D
4 

 ND
5  
2
Scaling relationships for turbomachines of
the same geometry (=geometrical similarity)
For a change in
diameter only
Q2 D2

Q1 D1
3
H 2  D2 


H1  D1 
P2  D2 


P1  D1 
For a rotational speed
change only
Q2 N 2

Q1 N1
2
35
H 2  N2 


H1  N1 
P2  N 2 


P1  N1 
3
2
Pumps in series and parallel
Series
Equivalent pump
Parallel
Equivalent pump
Pumps in Series
Add the heads
(H) at each flow
rate (Q)
For example, for
two identical
pumps the head
will be double
that of a single
pump.
Pumps in Parallel
Add the flow
rates (Q) at each
head (H)
For example, for
two identical
pumps the flow
rate will be
double that of a
single pump.
Pump-system operation
System resistance (losses)
curves (typically H  Q2)
C = operating point
Jet propulsion
History – Before Turbojets
Thermojet
Henri Coandă
1910
Aeolipile
Rocket
Hero of
Alexandria
Chinese Taoist Chemists
75 A.D.
1st Century
History – The First Jets
Hans Von Ohain
Frank Whittle
Test engine - 1937
Test engine - 1935
He S-3 - 1938
W.1 Turbojet - 1939
History – More Modern Jets
Centrifugal Compressor
Turbojet
Axial Flow Compressor
Turbojet
- Used by Whittle & Ohain
- Introduced by Anselm Franz
(Junkers' Engine Div.) ~ 1944
- Short and fat
- Must bend the airflow
- Long and thin
- Improved airflow
Jet Types and Uses
Type
Description
Advantages
Disadvantages
Thermojet
A piston engine is used to run
the compressor. Works
like a regular turbojet
minus the turbines.
Turbojet
Generic term for simple
turbine engine
Simplicity of design
Very basic. Does not take
advantage of improved
efficiency of other designs.
Turbofan
Uses an enlarged first stage
compressor as a 'fan' to
provide more thrust.
Quieter, more
efficient for
subsonic
airspeeds.
More complex, large diameter,
heavy, subject to foreign
object damage.
Ramjet
No moving parts. Intake air is
compressed by the
airspeed and duct shape.
Lightweight, efficient
above Mach 2.0.
Needs high speed to operate, only
efficient in a narrow speed
range, used as accessory?
Turboprop
Not really a jet. A gas turbine
driving a propeller.
High efficiency at
low speed (300450 knots)
Limited top speed, noisy, complex
propeller drive and gearbox.
Propfan
Turboprop engine with one or
more propellers. Like a
turbofan without ducts.
Very high fuel
efficiency,
higher speed.
Very complex, more noisy than
turbofans.
Scramjet
Intake air is compressed but
not slowed to subsonic.
Intake, combustion and
exhaust occur in a single
constricted tube
Operates at very
high speed
(Mach 8-15).
Still in development. Need to be
above Mach 6 to operate.
Cooling problems.
Heavy, inefficient and
underpowered
Principles - Physical
Major Components of a Jet Engine
• Fan
• Compressor
• Combustor
• Turbine
• Mixer / Nozzle
Principles - Physical
• Newton’s 3rd Law of Motion:
– For every action there is an equal and
opposite reaction.
• Boyle’s Law:
– there is a relationship between the
pressure of a fixed amount of air and its
volume.
Principles - Physical
• Power is measured in pounds (lb) of thrust
(or Newtons of thrust: 4.45 N=1 lb).
• 1 lb of thrust means that the engine will be
able to accelerate one pound of material at
32 ft/s2.
• Approximate equation for net thrust of a jet
engine:
Fn  m V jfe  Va 
Principles - Chemical
• Kerosene is usually used to power Jets
in the form of Avtur, Jet-A, Jet-A1, Jet-B,
JP-4, JP-5, JP-7, or JP-8.
• Kerosene is obtained from the fractional
distillation of petroleum at 150°C and
275°C
• Kerosene consists of carbon chains
from the C12 to C15 range.
Principles - Thermodynamic
Efficiency
• Thermal Efficiency:
– 45% - 50% for today’s best engines.
• Propulsive Efficiency:
– About 47% for low by-pass turbojets.
– About 80% for high by-pass turbofans.
• Overall Efficiency:
– About 40% for modern jets at cruise
speed.
Future of Jets ?
• Small, personal jet aircraft using highly
efficient jet engines.
• High speed, high altitude jet aircraft.
– Engines to be cooled by new coal derived
jet fuel.
Future of Jets ?
• MEMS Turbines (Power on a Chip):
– Turbine blades span an area smaller than a
dime.
– Run for 10+ hrs on a container of diesel fuel
about as big as a D battery.
– Also could be used to power tiny planes for
the military
– 15W to 20W output.
• Flying humans:
– Tiny jet engines combined with a wing-suit.