Embed Size (px)
Citation preview
KHAIRUL IMRAN BIN SAINAN
T1-14-6A
03-55432863
013-3153413
COMPRESSIBLE FLOW
TURBOMACHINERY
THE DIFFERENTIAL APPROACH TO FLOW ANALYSIS
POTENTIAL FLOW
FLOW PAST IMMERSED BODIES
INTRODUCTION
CHAPTERS
CO1
[PO1, LO1] {C3}
CO2
[PO3, LO3,SS1] {C4}
CO3 [PO3, LO3,SS1] {C4}
Express differential form of conservation equations which describe fluid motion
Formulate specific equation to model the physical domain
Compose solutions for the mathematical models and deduce appropriate results for the physical domain
Contd…
CO4
[PO10, LO7,SS5]
{P4,A3}
Complete investigative assignment on selection of physical problem and solutions scheme
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
Review of thermodynamics principles
One dimensional compressible flows
Stagnation properties
Speed of sound & Mach No.
One dimensional isentropic flows
Variation of fluid velocity with change of area
Isentropic flows through nozzles
- converging nozzles
- converging diverging nozzles
CHAPTER CONTENTS
FUEL CELL MODELING
Flows involve significant density variations: compressible
flow
Deals with high velocity of fluid motions
Involve thermodynamics properties fundamentals
Considers the effect of kinetic energy which cannot be
neglected
Potential energy may still negligible
WHAT IS?
FUEL CELL MODELING
Analyzing in one dimensional sense
Ideal gas
Constant specific heat
ASSUMPTIONS
FUEL CELL MODELING
Internal Flows
External Flows
FUEL CELL MODELING
Pressure (P), denstiy (ρ) and temperature (T) are related
into:
287 J/kgK (unique gas constant)
Kelvin
kg/m3
(1)
The static enthalpy is defined as:
(2)
Pressure
Internal
energy
Static Enthalpy
FUEL CELL MODELING
Put (1) into (2)
(3)
The internal energy may express as a function of 2
independent properties
where
Differentiate,
(4)
m3/kg
FUEL CELL MODELING
Therefore,
Specific heat of constant volume:
(6)
(5)
Combine (6) into (5)
(7)
Constant
volume
FUEL CELL MODELING
Specific heat of constant pressure:
(8)
Differentiate ,
(9)
Meanwhile enthalpy is a function of 2 properties:
Combine (9) into (8)
(10)
Constant
pressure
Combine (10) & (7) into (4)
Assume constant temperature:
(11)
(12)
FUEL CELL MODELING
FUEL CELL MODELING
Specific heat ratio:
(13)
Therefore,
FUEL CELL MODELING
Stagnation Process:
Define as the process when the fluid is stagnated or brought
to stop which is V = 0
The properties of a fluid at the stagnation state are called
stagnation properties (stagnation temperature, stagnation
pressure, stagnation density, etc.).
FUEL CELL MODELING
Enthalpy represents the total energy of fluid in absence of
kinetics & potential energies (1st Law of Thermodynamics)
At high speed flows the potential energy may neglected
however the kinetics energy must be considered
Combination of enthalpy and KE is called stagnation
enthalpy (or total enthalpy) KE
Static enthalpy
Stagnation
enthalpy
(kJ/kg)
(1)
FUEL CELL MODELING
The actual state, actual stagnation
state, and isentropic stagnation
state of a fluid on an h-s diagram.
FUEL CELL MODELING
Consider steady flow through
a duct (no shaft work, heat
transfer) Q = 0
Therefore the steady flow
equations becomes:
If no heat and work involves in the system
the stagnation enthalpy is constant
Stagnation enthalpy:
Not applicable if turbine
and compressor is exist.
FUEL CELL MODELING
What happen if we consider V2=0
Stagnation enthalpy:
The enthalpy of a fluid
when adiabatically or
isentropically brought
to rest or V = 0.
During this process (stagnation), the kinetic energy
of a fluid is converted to enthalpy, which results in an
increase in the fluid temperature and pressure.
FUEL CELL MODELING
Assume ideal gas and constant specific heat
(2)
(3)
Combine (2) into (1)
Stagnation
Temperature Dynamic Temperature
Static
Temperature
FUEL CELL MODELING
Stagnation (or total) temperature T0 : It represents the
temperature an ideal gas attains when it is brought to rest adiabatically.
Dynamic temperature: V2/2cp : corresponds to the
temperature rise during such a process.
FUEL CELL MODELING
The pressure of fluid attains when brought to rest
isentropically called as stagnation pressure
Stagnation
Pressure Dynamic Pressure
Static
Pressure
Dynamic pressure: ½ ρV2 : corresponds to the pressure rise
during such a process.
FUEL CELL MODELING
For Ideal Gas, based on isentropic process the stagnation
process:
Similarly for stagnation density:
IMPORTANT:
-Stagnation enthalpy and stagnation temperature will never be change as long as
no heat and work transfer across the system boundaries
- However stagnation pressure may change
FUEL CELL MODELING
Stagnation pressure may change
The actual state, actual stagnation
state, and isentropic stagnation
state of a fluid on an h-s diagram.
The stagnation pressure may
change due to friction, pressure
losses which is irreversible
The process is considered as
non-isentropic process
P0 Change
FUEL CELL MODELING
Air at 320K is flowing in a duct at a
velocity (a) 1 , (b) 10, and (c) 100 m/s.
Determine the readings of the thermometer
Assumptions: The stagnation process is isentropic
Solutions:
Analysis: The air that strikes the probe will be brought to a
complete stop thus undergo stagnation process. Thermometer
sense this stagnated air which is stagnation temperature, T0
= 1.005 kJ/kgK
(a) = 320.0 K
(b) = 320.1K
(c) = 325 K
FUEL CELL MODELING
Calculate the stagnation temperature and pressure for
(a) Helium at 0.25 MPa, 500C and 240 m/s
(a) Steam at 0.1 MPa, 3500C and 480 m/s
Solutions:
Assumptions: The stagnation process is isentropic and Steam
and Helium are ideal gas
= 5.1926 kJ/kgK k = 1.667
= 1.865 kJ/kgK k = 1.329
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
Speed of sound is pressure wave which travel through a
medium
For an ideal gas, the speed of sound:
287 J/kgK
Temperature
1.4
Mach No: Sonic
Subsonic
Supersonic
FUEL CELL MODELING
Area and Mach No relation. what is ? significance ?
Derivation
Step 1: Consider mass balance of steady flow process
Step 2: Differentiate eqn. 1 and divide by mass flow rate
(1)
(2)
FUEL CELL MODELING
Step 3: In steady flow; W, Q, KE and PE assume as 0
Step 4: From 2nd Gibbs equation of entropy
or (3)
(4)
Step 5: In isentropic flows, Tds = 0; Therefore,
(5)
since
FUEL CELL MODELING
Step 6: Combine (5) into (3)
Step 7: Combine (6) into (2)
(6)
(7)
Step 8: Since,
= (8)
FUEL CELL MODELING
Step 9: Combine (8) into (7)
(9)
Step 10: Eqn. 9 can be arrange into
(10)
This equation governs the subsonic and supersonic flows for both diffusers and
nozzles
(11)
Finally
FUEL CELL MODELING
Conclusion:
(Subsonic)
(Supersonic)
(Sonic)
To accelerate fluid, converging nozzles is needed if the flow
is subsonic and diverging nozzles if the flow is supersonic
In converging nozzles highest velocity is sonic
In Converging-diverging nozzles is needed to accelerate
fluid to supersonic
FUEL CELL MODELING
In Summary:
1. For Converging nozzle:
FUEL CELL MODELING
2. Flow properties in nozzles and diffusers
-Nozzle function: to increase the velocity
-Diffuser function: to reduce the velocity
FUEL CELL MODELING
When Mat = 1, the properties at the nozzle
throat become the critical properties.
FUEL CELL MODELING ISENTROPIC FLOW THROUGH converging NOZZLES
Effect of Pb on converging nozzle
Mass flow rate through a nozzle
Maximum mass flow rate
FUEL CELL MODELING
The effect of back pressure Pb on the
mass flow rate and the exit pressure Pe
of a converging nozzle.
The variation of the mass flow rate through
a nozzle with inlet stagnation properties.
FUEL CELL MODELING
Relation between flow area A throughout nozzle and throat area A*
Relation between flow area Ma throughout nozzle and throat area A*
Ma* is the local velocity
nondimensionalized with respect
to the sonic velocity at the throat.
Ma is the local velocity
nondimensionalized with respect
to the local sonic velocity.
Table A-13
FUEL CELL MODELING
At Converging nozzle: A decrease; P decrease; T decrease; ρ decrease; V increase;
Ma increase
At Throat: critical-pressure value occurs (Ma = 1)
At Diverging nozzle: A increase; P decrease; T decrease; ρ decrease; V increase;
Ma increase
IMPORTANT:
-In order to achieve supersonic Mach. No; converging-diverging nozzle is needed
with correct back pressure Pb
-Converging nozzle only gives Mach No. = 1
-Diverging nozzle alone will not attains the supersonic velocity.
FUEL CELL MODELING
Effect of Pb on converging-
diverging nozzle
FUEL CELL MODELING
FUEL CELL MODELING
Tutorial 1
Air enters a converging diverging nozzle at 800 kPa with
specific heat ratio of k = 1.4. Determine the pressure at the
throat area.
FUEL CELL MODELING
Tutorial 2
Solve the exit velocity for the nozzle shown:
Assume isentropic flow
T1 = 350K P1 = 1 MPa
P2 = 100kPa
Mat = 1
k = 1.4
FUEL CELL MODELING
FUEL CELL MODELING
Tutorial 3
Quiescent carbon dioxide at a given inlet temperature of 400K
and pressure of 1.2MPa is accelerated at Mach No. 0.6.
Determine the temperature and pressure after acceleration.
FUEL CELL MODELING
FUEL CELL MODELING
Tutorial 4
Helium enters a converging diverging nozzle at temperature of
800K , velocity of 100 m/s and pressure 0.7MPa.
Determine the lowest temperature and pressure at the throat
Assume k = 1.667 and Cp = 5.1926 kJ/kgK
FUEL CELL MODELING
FUEL CELL MODELING
Tutorial 1
Determine the air speed of a scramjet engine at Mach No. 7
with air temperature of -200C
R = 0.287 kJ/kgK k =1.4
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
Normal shock waves: The shock waves that occur in a plane
normal to the direction of flow. The flow process through the
shock wave is highly irreversible.
Normal shock occurs when the flow
is supersonic
FUEL CELL MODELING
FUEL CELL MODELING
Conservation of mass
Conservation of energy
Conservation of momentum
Increase of entropy
Area is same because NS
occurs within thin line
FUEL CELL MODELING
Fanno line:
Combining the conservation of mass
and energy relations into a single
equation and plotting it on an h-s
diagram yield a curve. It is the locus
of states that have the same value
of stagnation enthalpy and mass
flux.
Rayleigh line:
Combining the conservation of mass
and momentum equations into a
single equation and plotting it on the
h-s diagram yield a curve.
FUEL CELL MODELING
The relations between various properties before and after the shock for an ideal gas
with constant specific heats
upstream
downstream
FUEL CELL MODELING
Area consider same
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
When the space shuttle travels at supersonic speeds through the atmosphere, it
produces a complicated shock pattern consisting of inclined shock waves called
oblique shocks.
Some portions of an oblique shock are curved, while other portions are straight.
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
Turbomachines: Pumps and turbines in which energy is supplied or extracted by a
rotating shaft.
The words turbomachine and turbomachinery are often used in the literature to
refer to all types of pumps and turbines regardless of whether they utilize a rotating
shaft or not.
• 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
OBJECTIVES:
FUEL CELL MODELING
Pumps:
-Energy absorbing devices
-energy is supplied
-transfer energy to the fluid
-the increase in fluid energy is
felt as increase in pressure of
the fluid.
Turbines:
-Energy producing devices
-extract energy from fluid
-transfer that energy to
mechanical output
-The fluid at outlet suffers an
energy loss in the form of a
loss of pressure.
FUEL CELL MODELING
The purpose of a pump is to add
energy to a fluid, resulting in an
increase in fluid pressure, not
necessarily an increase of fluid
speed across the pump.
The purpose of a turbine is to
extract energy from a fluid,
resulting in a decrease of fluid
pressure, not necessarily a
decrease of fluid speed across
the turbine.
For steady flow,
mass flow out = mass flow in
For incompressible flow,
Dout = Din, Vout = Vin, but Pout > Pin.
FUEL CELL MODELING
When used with gases, pumps are called fans, blowers, or compressors, depending
on the relative values of pressure rise and volume flow rate.
Fan: relatively low pressure rise and high flow rate. Examples include ceiling fans,
house fans, and propellers.
Blower: relatively moderate to high pressure rise and moderate to high flow rate.
Examples include centrifugal blowers and squirrel cage blowers in automobile
ventilation systems, furnaces, and leaf blowers.
Compressor: designed to deliver a very high pressure rise, typically at low to
moderate flow rates. Examples include air compressors that run pneumatic tools and
inflate tires at automobile service stations, and refrigerant compressors used in heat
pumps, refrigerators, and air conditioners.
FUEL CELL MODELING
Fluid machines may also be broadly classified as either positive-displacement
machines or dynamic machines, based on the manner in which energy transfer
occurs.
In positive-displacement machines: Fluid is directed into a closed volume. Energy
transfer to the fluid is accomplished by movement of the boundary of the closed
volume, causing the volume to expand or contract, thereby sucking fluid in or
squeezing fluid out, respectively.
Dynamic machines: There is no closed volume; instead, rotating blades supply or
extract energy to or from the fluid.
For pumps, these rotating blades are called impeller blades, while for turbines, the
rotating blades are called runner blades or buckets.
Examples of dynamic pumps include enclosed pumps and ducted pumps and
open pumps.
Examples of dynamic turbines include enclosed turbines, such as the
hydroturbine that extracts energy from water in a hydroelectric dam, and open
turbines such as the wind turbine that extracts energy from the wind.
FUEL CELL MODELING
-The mass flow rate of fluid through the pump is an obvious primary pump performance
parameter.
-For incompressible flow, it is more common to use volume flow rate rather than mass
flow rate.
-In the turbomachinery industry, volume flow rate is called capacity and is simply mass
flow rate divided by fluid density,
-The performance of a pump is characterized additionally by its net head H,
defined as the change in Bernoulli head between the inlet and outlet of the pump:
FUEL CELL MODELING
FUEL CELL MODELING
For the case in which a liquid is being pumped,
the Bernoulli head at the inlet is equivalent to
the energy grade line at the inlet.
The net head of a pump, H, is defined as the
change in Bernoulli head from inlet to outlet;
for a liquid, this is equivalent to the change in
the energy grade line, H = EGLout - EGLin,
relative to some arbitrary datum plane; bhp is
the brake horsepower, the external power
supplied to the pump.
FUEL CELL MODELING
1. Pump performance VS Piping Requirement
FUEL CELL MODELING
Free delivery: Max volume flow rate when its net head is zero, H = 0
Shutoff head: The net head when the volume flow rate is zero which achieved when the outlet port
is blocked off. H is large but V is zero; the pump’s efficiency is zero
Best Efficiency Point (BEP): Max efficiency & notated by an asterisk (H*, bhp*, etc.).
Pump Performance Curves (or characteristic curves): Curves of H, pump, and bhp as functions of
volume flow rate.
Operating point or duty point of the system: In a typical application, Hrequired and Havailable match at
one unique value of flow rate—this is the operating point or duty point of the system.
For steady conditions, a pump can operate only along its performance curve.
FUEL CELL MODELING
It is common practice in the pump industry to offer
several choices of impeller diameter for a single
pump casing.
(1) reduce manufacturing costs
(2) increase capacity by simple impeller replacement
(3) to standardize installation mountings
(4) reuse of equipment for a different application
2. Impeller Dia. VS Piping Requirement
FUEL CELL MODELING
3. Cavitations & Net Positive Suction Head
Local pressure fall below the vapor
pressure of the liquid, Pv.
When P < Pv, vapor-filled bubbles
called cavitation bubbles appear.
Net positive suction head (NPSH):
The difference between the pump’s
inlet stagnation pressure head and
the vapor pressure head.
FUEL CELL MODELING
The volume flow rate at which the actual
NPSH and the required NPSH intersect
represents the maximum flow rate that
can be delivered by the pump without
the occurrence of cavitation.
Required net positive suction head (NPSHrequired): The minimum NPSH
necessary to avoid cavitation in the pump.
FUEL CELL MODELING
4. Pumps Configuration
-At low values volume flow rate, Hcombined = H1 + H2 + H3
-However individual pump must be bypassed if the volume flow rate is running larger
than the design free delivery flow rate
FUEL CELL MODELING
4. Pumps Configuration
-At high values volume flow rate, Qcombined = Q1 + Q2 + Q3
-However individual pump must be bypassed if the system is running larger than the
design shutoff head
FUEL CELL MODELING
-Involve rotating blades called impeller blades or rotor blades, which impart momentum
to the fluid.
-Sometimes called rotodynamic pumps or simply rotary pumps.
-Rotary pumps are classified by the manner in which flow exits the pump:
(a) centrifugal flow, (b) mixed flow and (c) axial flow
FUEL CELL MODELING
Centrifugal-flow Pump:
Fluid enters axially (in the same direction as the axis of the rotating shaft) in the
center of the pump, but is discharged radially (or tangentially) along the outer
radius of the pump casing. Centrifugal pumps are also called radial-flow pumps.
Axial-flow Pump:
Fluid enters and leaves axially, typically along the outer portion of the pump
because of blockage by the shaft, motor, hub, etc.
Mixed-flow Pump:
Intermediate between centrifugal and axial, with the flow entering axially, not
necessarily in the center, but leaving at some angle between radially and
axially.
FUEL CELL MODELING
r1 and r2 as the radial locations of the impeller blade inlet and outlet
b1 and b2 are the axial blade widths at the impeller blade inlet and outlet
FUEL CELL MODELING
FUEL CELL MODELING
-V1, n and V2, n are defined as average normal (radial) components of velocity at radii r1 and r2.
-Absolute velocity vectors of the fluid are shown as bold arrows. It is assumed that the
flow is everywhere tangent to the blade surface when viewed from a reference frame
rotating with the blade, as indicated by the relative velocity vectors.
FUEL CELL MODELING
X2
X1
V1, t
FUEL CELL MODELING
= Outlet blade angle
= Inlet blade angle
b2 = Outlet blade height
b1 = Inlet blade height
= Normal (radial) outlet velocity
= Normal (radial) inlet velocity
X2
X1
V1, t
V1, t = Tangential inlet velocity
V2, t = Tangential outlet velocity
FUEL CELL MODELING
Volume flow rate: Euler turbomachine equation:
Brake horse power (Win) :
Shutoff Head:
Net Head:
Shaft Torque:
0
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
FUEL CELL MODELING
-impeller blades behave more like the wing of an airplane
-producing lift by changing the momentum of the fluid as they rotate.
-lift force on the blade is caused by pressure differences between the top and
bottom surfaces of the blade, and the change in flow direction leads to downwash
(a column of descending air) through the rotor plane.
-From a time-averaged perspective, there is a pressure jump across the rotor
plane that induces a downward airflow.
FUEL CELL MODELING
FUEL CELL MODELING
-Unlike centrifugal fans, brake horsepower tends to
decrease with flow rate.
-The efficiency curve leans more to the right
-Efficiency drops rapidly at higher volume flow rates
beyond the BEP.
-The net head curve also decreases continuously with
flow rate
-If head requirements not important, propeller fans is operated beyond BEP to achieve higher
volume flow rates.
-Since bhp decreases at high values of flow rate, there is not a power penalty when the fan is
run at high flow rates. For this reason it is tempting to install a slightly undersized fan and push
it beyond its best efficiency point.
-At the other extreme, if operated below its maximum efficiency point, the flow may be noisy
and unstable, which indicates that the fan may be oversized.
-It is usually best to run a propeller fan at, or slightly above, its maximum efficiency point.
FUEL CELL MODELING
(a) Tube-axial fan
(b) A second rotor rotates opposite direction
called a counter-rotating axial-flow fan
(c) A set of stator blades can be added either
upstream or downstream of the rotating
impeller.
FUEL CELL MODELING
106
PUMP SCALING LAWS
Dimensional analysis of a pump.
Dimensional analysis is useful for
scaling two geometrically similar
pumps. If all the dimensionless
pump parameters of pump A are
equivalent to those of pump B, the
two pumps are dynamically similar.
When plotted in terms of dimensionless
pump parameters, the performance curves
of all pumps in a family of geometrically
similar pumps collapse onto one set of
nondimensional pump performance curves.
Values at the best efficiency point are
indicated by asterisks.
108
When a small-scale model is
tested to predict the performance
of a full-scale prototype pump,
the measured efficiency of the
model is typically somewhat
lower than that of the prototype.
Empirical correction equations
such as Eq. 14–34 have been
developed to account for the
improvement of pump efficiency
with pump size.
109
Pump Specific Speed
Pump specific speed is used to characterize the
operation of a pump at its optimum conditions
(best efficiency point) and is useful for
preliminary pump selection and/or design.
Conversions between the dimensionless,
conventional U.S., and conventional
European definitions of pump specific
speed. Numerical values are given to four
significant digits. The conversions for
NSp,US assume standard earth gravity.
Maximum efficiency as a function of
pump specific speed for the three
main types of dynamic pump. The
horizontal scales show
nondimensional pump specific speed
(NSp), pump specific speed in
customary U.S. Units (NSp, US), and
pump specific speed in customary
European units (NSp, Eur).
111
Affinity Laws
Equations 14–38 apply to both pumps and
turbines.
States A and B can be any two homologous
states between any two geometrically
similar turbomachines, or even between two
homologous states of the same machine.
Examples include changing rotational
speed or pumping a different fluid with the
same pump.
112
TURBINES
The rotating part of a hydroturbine is called the runner.
When the working fluid is water, the turbomachines are called hydraulic turbines or
hydroturbines.
When the working fluid is air, and energy is extracted from the wind, the machine is
called a wind turbine.
Most people use the word windmill to describe any wind turbine, whether used to
grind grain, pump water, or generate electricity.
The turbomachines that convert energy from the steam into mechanical energy of a
rotating shaft are called steam turbines.
Turbines that employ a compressible gas as the working fluid is gas turbine.
113
Positive-Displacement Turbines
A positive-displacement turbine may be thought
of as a positive-displacement pump running
backward—as fluid pushes into a closed volume,
it turns a shaft or displaces a reciprocating rod.
The closed volume of fluid is then pushed out as
more fluid enters the device.
There is a net head loss through the positive-
displacement turbine; energy is extracted from
the flowing fluid and is turned into mechanical
energy.
However, positive-displacement turbines are
generally not used for power production, but
rather for flow rate or flow volume measurement.
114
Dynamic Turbines
Dynamic turbines are used both as flow measuring devices and as power generators.
Hydroturbines utilize the large elevation change across a dam to generate electricity, and
wind turbines generate electricity from blades rotated by the wind. There are two basic
types of dynamic turbine—impulse and reaction.
Impulse turbines require a higher head, but can operate with a smaller volume flow rate.
Reaction turbines can operate with much less head, but require a higher volume flow
rate.
115
Impulse Turbines
In an impulse turbine, the fluid is sent
through a nozzle so that most of its
available mechanical energy is converted
into kinetic energy.
The high-speed jet then impinges on
bucket-shaped vanes that transfer energy
to the turbine shaft.
The modern and most efficient type of
impulse turbine is Pelton turbine and the
rotating wheel is now called a Pelton
wheel.
116
117
Reaction Turbines
The other main type of energy-producing
hydroturbine is the reaction turbine, which
consists of fixed guide vanes called stay vanes,
adjustable guide vanes called wicket gates, and
rotating blades called runner blades.
Flow enters tangentially at high pressure, is
turned toward the runner by the stay vanes as it
moves along the spiral casing or volute, and
then passes through the wicket gates with a
large tangential velocity component.
A reaction turbine differs significantly
from an impulse turbine; instead of
using water jets, a volute is filled with
swirling water that drives the runner.
For hydroturbine applications, the axis
is typically vertical. Top and side views
are shown, including the fixed stay
vanes and adjustable wicket gates.
118
There are two main types of reaction turbine—Francis and Kaplan.
The Francis turbine is somewhat similar in geometry to a centrifugal or mixed-flow
pump, but with the flow in the opposite direction.
The Kaplan turbine is somewhat like an axial-flow fan running backward.
We classify reaction turbines according to the angle that the flow enters the runner. If
the flow enters the runner radially, the turbine is called a Francis radial-flow turbine.
If the flow enters the runner at some angle between radial and axial, the turbine is
called a Francis mixed-flow turbine. The latter design is more common.
Some hydroturbine engineers use the term ―Francis turbine‖ only when
there is a band on the runner. Francis turbines are most suited for heads that lie
between the high heads of Pelton wheel turbines and the low heads of Kaplan turbines.
A typical large Francis turbine may have 16 or more runner blades and can achieve a
turbine efficiency of 90 to 95 percent.
If the runner has no band, and flow enters the runner partially turned, it is called a
propeller mixed-flow turbine or simply a mixed-flow turbine. Finally, if the flow is turned
completely axially before entering the runner, the turbine is called an axial-flow turbine.
Reaction Turbines
Kaplan turbines are called double regulated because the flow rate is controlled in two
ways—by turning the wicket gates and by adjusting the pitch on the runner blades.
Propeller turbines are nearly identical to Kaplan turbines except that the blades are
fixed (pitch is not adjustable), and the flow rate is regulated only by the wicket gates
(single regulated).
Compared to the Pelton and Francis turbines, Kaplan turbines and propeller turbines
are most suited for low head, high volume flow rate conditions.
Their efficiencies rival those of Francis turbines and may be as high as 94 percent.
120
Relative and absolute velocity
vectors and geometry for the
outer radius of the runner of a
Francis turbine. Absolute velocity
vectors are bold.
Relative and absolute velocity vectors
and geometry for the inner radius of
the runner of a Francis turbine.
Absolute velocity vectors are bold.
121
Typical setup and terminology for a hydroelectric plant
that utilizes a Francis turbine to generate electricity;
drawing not to scale. The Pitot probes are shown for
illustrative purposes only.
The net head of a turbine is defined as the difference
between the energy grade line just upstream of the turbine
and the energy grade line at the exit of the draft tube.
122
By definition, efficiency must
always be less than unity.
The efficiency of a turbine is
the reciprocal of the
efficiency of a pump.
(a) An aerial view of Hoover Dam and (b) the top
(visible) portion of several of the parallel electric
generators driven by hydraulic turbines at Hoover
Dam.
123
14–5 ■ TURBINE SCALING LAWS
The main variables used for
dimensional analysis of a turbine.
The characteristic turbine diameter
D is typically either the runner
diameter Drunner or the discharge
diameter Ddischarge.
124
Dimensional analysis is useful for
scaling two geometrically similar
turbines. If all the dimensionless
turbine parameters of turbine A are
equivalent to those of turbine B, the
two turbines are dynamically similar.
In practice, hydroturbine engineers
generally find that the actual increase in
efficiency from model to prototype is only
about two-thirds of the increase given by
this equation.
125
Turbine Specific Speed
A pump–turbine is used by
some power plants for energy
storage: (a) water is pumped
by the pump–turbine during
periods of low demand for
power, and (b) electricity is
generated by the pump–
turbine during periods of high
demand for power.
126
Maximum efficiency as a function of turbine specific speed for the three main
types of dynamic turbine. Horizontal scales show nondimensional turbine specific
speed (NSt) and turbine specific speed in customary U.S. units (NSt, US). Sketches
of the blade types are also provided on the plot for reference.
