Transcript Class01 Intro Units

Turbomachinery
Lecture 1
- Pumps, Turbines
- Subcomponents
- Units, Constants, Parameters
- Thermodynamics
www.engr.uconn.edu/barbertj~
- ME3280 / ME6160
1
Turbomachinery
• Turbomachine: A device in which energy is transferred to
or from a continuously flowing fluid through a casing by
the dynamic action of a rotor.
• Rotor or impellor: Changes stagnation enthalpy of fluid
moving through it by either doing positive or negative
work.
• Works on fluid to produce either power or flow
• Turbomachine categories:
– Those which absorb power to increase fluid pressure
or head [compressor, pump].
• Fan: pressure rise up to
• Blower: pressure between
• Compressor: pressure rise
1 lbf/in2
1 - 40 lbf/in2
above 40 lbf/in2
– Those which produce power by expanding fluid to
lower pressure or head [turbine].
2
Turbomachinery
• Turbomachine classification
– Impulse: pressure change takes place in one or more
nozzles
– Reaction: takes place in all nozzles
• Path of through flow
– Mainly or wholly parallel to axis of rotation: axial flow
machine
– Mainly or wholly in a plane perpendicular to axis of
rotation: radial flow machine
3
Brayton Thermodynamic Cycle for Single Spool Turbojet Engine
4
Meridional Projection of Axial & Centrifugal Compressor Stages
Essentially constant radius
Substantial change in radius
5
Turbomachinery - Pumps
• Positive Displacement: moving boundary forces fluid
along by volume changes.
– Reciprocating, rotary: piston, screw, ...
• Dynamic: momentum change by means of moving
blades or vanes (No closed volume).
– Axial, centrifugal, mixed
– Fluid increases momentum while moving through open
passages and then converts high velocity to pressure rise in
diffuser section
• In radial machines doughnut-shaped diffuser is called a
scroll
• Through a casing...........Not wind mills, water wheels or
propellers
• Flow conditioning..........Stators, scrolls
6
Turbomachinery - Pumps
Screw
Centrifugal
Axial
7
Turbomachinery - Turbines
• Extracts energy from a fluid with high head
[pump run backwards].
• Reaction turbine: fluid fills blade passages
and pressure drop occurs within impeller.
– Low-head, high-flow devices
– V across rotor increases, p decreases
– Stators merely alter direction of flow
• Impulse turbine: converts high head to high
velocity using a nozzle; then strikes blades
as they pass by.
– Impeller passages are not fluid filled, and jet
flows past blades is essentially at constant
pressure.
– Discharge velocity  relative inlet velocity
across rotor
– no net change in p across rotor
– stators shaped to increase V, decrease p
8
Gas Generator
• Purpose: Supply High-Temperature and
High-Pressure Gas
– compressor, combustor, turbine
9
Turbojet
• Purpose: Provide High-Velocity Thrust
– inlet, compressor, combustor, turbine, nozzle
10
Turbofan
• Purpose: Produce Lower-Velocity Thrust
Through the Addition of a Fan
– inlet, fan, compressor, combustor, turbine, nozzle
Stations
0=1= Upstream
2 =compressor inlet
2.5=low-to-high comp
3 =combustor inlet
4 =turbine inlet
4.5=high-to-low turb.
5 =nozzle inlet
8 =exit
11
Turboprop
• Purpose: Produce Low-Velocity Thrust Through
Addition of a Propeller
12
Turboshaft
• Purpose: Produce Shaft Power for Rotating
Component [Not for Thrust] - helicopter
13
Low BPR
14
BPR= mass flow through bypass/mass flow through core
High BPR
15
Gas Turbine Components
• Main Flow-Path
Components of a Gas
Turbine Engine:
–
–
–
–
–
inlet
compressor
combustor
turbine
nozzle
• Secondary Flow-Path
Components:
– disk cavities
– cooling flow bleed ducts
– bearing compartments
16
Inlet
• Inlet Reduces the Entering Air Velocity to a Level
Suitable for the Compressor
• Often Considered Part of Nacelle
Nacelle
• Critical Factors:
– Mach Number
– Mass Flow
– Attached Flow
• Subsonic Inlet
– Divergent area used
to reduce velocity
• Supersonic Inlet
– Shocks often used to
achieve reduced velocity
and compression
Engine Inlet
17
Fan/Compressor
• Axial-Flow Fan
• Axial-Flow Compressor
– Low-Pressure
– High-Pressure
• Centrifugal Compressor
– Mixed Axial/Radial Flow
Fan
Low-Pressure
Compressor
18
High-Pressure
Compressor
Combustor
• Designed to Burn a Mixture of Fuel & Air
and Deliver to Turbine
– Uniform Exit Temperature
– Complete Combustion
– Emission issues
– Exit Temperature Must Not Exceed
Critical Limit Set By Turbine Metal +
Cooling Design
Combustor
19
Turbine
• Extracts Kinetic Energy from
expanding gases and
converts to shaft HP to drive
compressor/fan
– Axial Flow Turbine
• High Flow Rates
• Low-Moderate Pressure
Ratios
High-Pressure
Turbine
– Centrifugal Turbine
• Lower Flow Rates
• Higher Pressure Ratio
20
Low-Pressure
Turbine
Nozzle
• Increase velocity of exhaust before discharge from
nozzle and straighten flow from turbine
– Convergent Nozzle Used When Nozzle Pr < 2
(Subsonic Flow)
– Convergent-Divergent Nozzle Used When Nozzle Pr > 2
• Often incorporate variable geometry to control throat area
Nozzle
21
3 Planar Views of
a Turbomachine
Cross Flow Area Variation in Compressor & Turbine Rotors
Diffuser
Cross Flow Area
Nozzle
23
Favorable [Turbine] & Unfavorable [Compressor] Pressure Gradients
Bernoulli: dp
dV
24
Thermophysical Process
Across an Adiabatic
Stator
Turbine
Compressor
25
Compressibility Can Be A Major Issue in Nozzle Flows
Subsonic
M  1,
Subsonic
M  1,
Supersonic nozzle
dA
0
A
Subsonic diffuser
dA
0
A
26
Gas-Turbine Design Process
Well Developed
Developed Fairly Mature
Developed Improvements
Required
Determine “Steady” and Unsteady Coupling
Effects Between the Components
Determine Unsteady-Flow Interaction
Effects on Performance (e.g.. Wake /
Blade, Shock / Blade, Potential,
Thermal, and Structural Interactions
Under
Development
Multi-Component 3-D Steady
and Unsteady-Flow Analysis
Multi-Stage Turbomachinery 3-D
Unsteady-Flow Analysis
Multi-Stage Turbomachinery and Secondary
Flow Path 3-D Steady-Flow Analysis
3-D Turbomachinery Airfoil and
Design and Analysis
Turbomachinery 2-D Airfoil
Section Design and Analysis
Through-Flow or Streamline
(2D x,r) Analysis
Turbomachinery
Meanline (1D) Analysis
Engine Cycle Analysis
Determine Primary Blade-Row
and Secondary Flow Path
Pressure and Mass-Flow
Distribution Interaction Effects
Upon Stacking Airfoil Sections from Structural
or Aero Considerations, Determine Single BladeRow Performance (i.e.. Loading and Pt Losses)
and Combustor Heat and NOx Release
From Velocity Triangles, Determine Airfoil
Shape as a Function of Radius for Required
Flow Turning and Pressure Rise/Drop
From Radial Equilibrium or Axisymmetric
Streamline Analysis, Determine Spanwise
Variation in Velocity Triangles
From Required Compressor / Turbine Work
Determine Number of Stages and Velocity
Triangles of”Mean Radius” Streamline
From Required Thrust, Determine Work
Required by Compressor and Turbine and Heat
Addition from Combustor
Fidelity / Complexity
27
Units and Key Constants
28
• Conventional Units
Parameter
English Units
SI Units
–
–
–
–
Feet, Inches
Seconds
Pounds (force), lbf
psf, psi
Meters, M
Seconds, s
4.448 Newton, N
Pascal, Pa (1N/1m2)
bar (105Pa)
2.989 kPa
0.4536 kilogram
Joule, J
0.7457 kWatt
Distance
Time
Force
Pressure
– Mass
– Energy
– Power
1 ft H2O
Pounds (mass), lbm
Btu
1 Hp
29
Equivalent Systems of Units
System
English Eng.
English Gravitational
Metric
Metric
International System (SI)
Force Mass
lbf
lbm
lbf
slug
kgf
kg
dyne
gm
Newton
kg
Length
ft
ft
m
cm
m
time
s
s
s
s
s
1 Newton = 1 kg-m/sec2
1 Joule = 1 N-m/sec
30
Important Constants for Air
Variable
pressure
density
Universal gas
constant
Spec. gas constant
(air)
Air
Air
Joule constant
speed of sound
Symbol
p


R=/M
Cp
Cv
J
a
lbm unit
lb/ft2
slug/ft3
4.97+4
ft-lb/slug-mole-R
1716
ft-lb/slug-R
7.73
5.5
778.16 ft-lbf/BTU
1100 ft/s
lbf unit
lb/ft2
lbm/ft3
1545.33
ft-lb/lbm-mole-R
53.35
ft-lb/lbm-R
0.24
0.172
kg u
N/m
N/m
831
J/kg-mo
287
J/kg
1.00
0.71
1100 ft/s
440 m
R=287 J/kg-R = 287 m2/s2-K
31
Useful Equivalents
Quantity
Original Unit
Flow
Specific Energy
Mass
Rotational speed
Kinematic viscosity
Pressue
1.0
1.0
1.0
1.0
1.0
1.0
1 Joule
1 BTU
1 slug
cfs [ft3/sec]
ft2/s2
slug
rad/s
ft2/s
in. H2O
Equivalent
448. gal/min
1.0 ft-lbf/slug
32.174 lbm
9.549 rev/min
92,903 centistokes
5.2 lbf/ft2
= Nm =kg-m2/sec2
= 778.2 ft-lbf
= 32.2 lbm = lbf-sec2/ft
Atmospheric pressure
1 in Hg = 0.49116 psi
2116 psf = 14.7 psi = 1.013 Bar = 101,325 Pascals
32
SI – English Units
Runiv
J
kg  m2
 8314


2
kg  mole  K kg  sec  mole  K
Rspec
Runiv 8314
m2


 287 2
M
28.97
sec K
2
m
a 2   RT 
sec2
BTU
ft  lbf
ft  lbf
 1.987  778
 1545.3
mole  R
lbm  mole  R
lbm  mole  R
R
ft  lbf
Rspec  univ  53.35
M
lbm  R
ft  lbf
ft  lbm
ft 2
2
a   gRT    53.35
 32.2
 TR    1716  T 2
2
lbm  R
lbf  sec
sec
Runiv  1.987
33
• For Liquid Water :
  62.4lbm / ft 3
• U.S. Standard Atmosphere - 1976
lbf
pressure  14.696 2
in
temperature  518.67 R
34
Standard Atmosphere
http://www.digitaldutch.com/atmoscalc/tableatmosphere.htm
Altitude
Stratosphere
>65,000 ft
36,089 ft
59 F
Temperature
Altitude
36,089 ft
3.202 psia
14.696 psia
Pressure
35
36
37
Thermodynamics Review
38
Thermodynamics Review
• Thermodynamic views
– microscopic: collection of particles in random motion.
Equilibrium refers to maximum state of disorder
– macroscopic: gas as a continuum. Equilibrium is
evidenced by no gradients
• 0th Law of Thermo [thermodynamic definition of
temperature]:
– When any two bodies are in thermal equilibrium with
a third, they are also in thermal equilibrium with each
other.
– Correspondingly, when two bodies are in thermal
equilibrium with one another they are said to be at
the same temperature.
39
Thermodynamics Review
• 1st Law of Thermo [Conservation of energy]: Total work
is same in all adiabatic processes between any two
equilibrium states having same kinetic and potential
energy.
– Introduces idea of stored or internal energy E
– dE = dQ - dW
• dW = Work done by system [+]=dWout= - pdV
• Some books have dE=dQ+dW [where dW is work done ON
system]
• dQ = Heat added to system [+]=dQin
– Heat and work are mutually convertible. Ratio of conversion is
called mechanical equivalent of heat J = joule
40
Review of Thermodynamics
• Stored energy E components
– Internal energy (U), kinetic energy (mV2/2), potential energy,
chemical energy
• Energy definitions
– Introduces e = internal energy = e(T, p)
– e = e(T)  de = Cv(T) dT thermally perfect
– e = Cv T
calorically perfect
• 2nd law of Thermo
– Introduces idea of entropy S
– Production of s must be positive
– Every natural system, if left undisturbed, will change
spontaneously and approach a state of equilibrium or rest. The
property associated with capability for change is called entropy.
dS 
 Qrev
T

TdS  dE  dW
41
Review of Thermodynamics
• Extensive variables – depend on total mass of the system, e.g. M, E,
S, V
• Intensive variables – do not depend on total mass of the system, e.g.
p, T, s,  (1/v)
• Equilibrium (state of maximum disorder) – bodies that are at the same
temperature are called in thermal equilibrium.
• Reversible – process from one state to another state during which the
whole process is in equilibrium
• Irreversible – all natural or spontaneous processes are irreversible,
e.g. effects of viscosity, conduction, etc.
42
Thermodynamic Properties
Derived
Primitive
Extensive
Intensive
Extensive
Intensive
Mass – M
Density - 
Energy – Eo
Specific energy – eo
-
Pressure – p
Kinetic energy – Ek
Sp. kin. energy – V2/2
-
Temperature – T
Potential energy – Ep
Sp. pot. energy – gz
Volume - V
Specific volume - 
Internal energy - E
Sp. int. energy - e
E0  E  Ek  E p
or
V2
e0  e 
 gz
2
 0   T  Total or stagnation state
43
1st Law of Thermodynamics
• For steady flow, defining:
V2 /2
gz
e
specific kinetic energy
specific potential energy
specific internal energy
h=e+pv  e+
p
specific enthalpy

V2
e0  e 
 gz
2
total specific energy
• We can write:
V2
e0  pv  e 
 gz  pv
2
• and
h  e  pv
and
h0  e0  pv
44
Equation of State
• The relation between the thermodynamic properties of a pure
substance is referred to as the equation of state for that substance, i.e.
F(p, v, T) = 0
• Ideal (Perfect) Gas
– Intermolecular forces are neglected
– The ratio pV/T in limit as p  0 is known as the universal gas
constant (R).
p  /T  R = 8.3143e3
– At sufficiently low pressures, for all gases
p/T = R
or
p   RT
• Real gas: intermolecular forces are important
45
Real Gas
 1150 R
46
Real Gas
47
1st & 2nd Law of Thermodynamics
• Gibbs Eqn. relates 2nd law properties to 1st law properties:
Tds  pdv  de
h  e  pv
dh  de  pdv  vdp
dp
Tds  dh 

48
Gibbs Equation
• Isentropic form of Gibbs equation:
dh 
dp

• and using specific heat at constant pressure:
RT
c p dT 
dP
P
dT R dP

T
cp P
49
Thermally & Calorically Perfect Gas
• Also, for a thermally perfect gas:
cP  cv  R
=
cp
cv
 -1 R


cp
dT   1 dP

T
 P
• Calorically perfect gas - Constant Cp
dT   1 dP
1 T   1 P
2
2
50
Isentropic Flow
• For Isentropic Flow:
 1 / 
T2  P2 
 
T1  P1 
or
T  CP 1 / 
• Precise gas tables available for design work –
Thermally Perfect Gas good for compressors not for
turbines because of burned fuel.
51
Gibbs Equation
• Rewriting Gibbs Equation:
Tds  dh 
dP
c p dT

1 RT dP
T
T P P
ds dT   1 dP


cP
T
 P
ds 

 T2    1  P2 
s2  s1
 ln   
ln  
cp

 T1 
 P1 
52
Gibbs Equation
• Rewriting Gibbs Equation:
Apply at stagnation state
 T02    1  P02 
s2  s1
 ln 
ln 


cp

 T01 
 P01 
For adiabatic processes, T0  constant
s2  s1
  1  P02 

ln 

cp

P
 01 
 P02 
 s2  s1 
1

  exp  

R 

 P01 
53
Mollier Chart for Air
3,000
P=50Atm
Temperature Deg R
2,500
Isobars are not parallel
20
2,000
10
1,500
5
2
1,000
500
0.00
1
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Entropy - BTU/Lbm/deg R
54
Mollier for Static / Total States
Poout
h02
1,650
h02i
We will soon see
1,450
P out
V2/2
2
V
h0  h 
2
1,250
T 1,050
Real
Ideal
850
Poin
650
h01
P in
450
-0.02
s
-0.01
0.00
0.01
0.02
S
0.03
0.04
0.05
0.06
55