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Last Rev.: 19 JUN 08Pelton Wheel: MIME 3470
~~~~~~~~~~~~~~MIME 3470Thermal Science Laboratory~~~~~~~~~~~~~~Laboratory . 11Pelton Wheel
Performance CharacteristicsStudents Names Section POINTS SCORETOTAL
PRESENTATIONApplicable to Both MS Word and Mathcad Sections
GENERAL APPEARANCE, ORGANIZATION, ENGLISH, & GRAMMAR5
ORDERED DATA, CALCULATIONS & RESULTSMATHCAD
DISCUSSION OF RESULTS
WHAT ARE TWO FEATURES OBSERVED FROM COMBINED PLOT?5
WHY IS THE BUCKET EXIT ANGLE SMALL AND NONZERO?5
WHAT IS PURPOSE OF CUTOUT AT BUCKET PERIPHERY? 5
WHAT IS THE MAXIMUM UTILIZATION FACTOR WHEN (2 = 0?5
Why must a turbine w/ nonzero have a rotor enclosed?5
Why does the relative velocity remain unchanged as
the flow passes through a Pelton bucket?5
ORIGINAL DATASHEET 5
MIME 3470Thermal Science Laboratory~~~~~~~~~~~~~~Laboratory . 11Pelton Wheel Performance Characteristics~~~~~~~~~~~~~~
Lab Partners: Name Name
NameNameSectionExperiment Time/Date:Time, date~~~~~~~~~~~~~~OBJECTIVEof this experiment is to plot the Pelton wheel actual and theoretical horsepowers vs. U/V1 (explained below) and to demonstrate that maximum power occurs when U/V1 ( 0.5. INTRODUCTIONA water turbine is a rotary engine that takes energy from moving water. The Pelton wheel is such a device. The earliest water turbines were water wheels which have been used for thousands of years for industrial power. Their main shortco-ming is size, which limits the flow rate and head that can be used.The migration from water wheels to modern, more efficient tur-bines took during the 19th century during the Industrial Revolution. Efficiency improvements of water turbines allowed them to compete with steam engines (wherever water was available). These turbines (using scientific principles, new materials, and, new manufacturing methods) were widely used for industrial power prior to electrical grids. Now they are mostly used for electric power generation. The main difference between early water turbines and water wheels is a swirl component of the water which passes energy to a spinning rotor. Swirl is the tangential velocity component induced by a curved impeller. This additional component of motion allowed the turbine to be smaller than a water wheel of the same power. They could process more water by spinning faster and could harness much greater heads. Later, impulse turbines such as the Pelton wheel were developed which did not use swirl. THEORY
Euler Turbine Equation
All turbines have a runner or rotor which holds the turbine vanes or blades. In the case of a water wheel, the vanes are simple paddles. This runner and attached vanes rotate as flowing water is directed onto the vanes. Since the runner is spinning, the imparted water force acting through a distance generates work. In this way, energy is transferred from the water flow to the turbine.
The basic design relationship for all turbomachines is very simple and is only a form of Newtons Laws of Motion applied to fluid traversing a rotor. Imagine water impinging on a turbine runner at Point 1 at some arbitrary angle and at rotor radius r1. Further, the fluid exits the runner at Point 2 having some other arbitrary angle and at rotor radius r2. Also, the flow is assumed to be an unchanging steady-state at every point in the system. The fluid velocity vector at any point can be resolved into three mutually perpendicular components:
Vaan axial component directed parallel to the axis of rotation,
Vma radial component directed radially outward from the axis of rotation, and
Vua tangential component directed parallel to the tangential velocity of the rotor, U.The change in magnitude in axial and radial components causes forces must be carried by the bearings. These forces, however, do not affect the angular rotation of the rotor except through bearing friction. However, the change in magnitude and of radius of the tangential velocity components corresponds to a change in angular momentum of the fluid and by Newtons Laws of Motion is equal to the summation of all the applied forces on the rotor; i.e., the net torque on the rotor, (. In general terms, this is as follows. If a mass of fluid M1 enters the rotor at radius r1, with tangential component of absolute velocity during time t; and, if during the same time t a mass M2 leaves the rotor at radius r2 with tangential component of absolute velocity ; then
For a unit mass steady flow, this becomes . For a steady rotor angular velocity of (, the rate of energy transferred or utilized Eutil = ((. Further, the linear velocity of the rotor is U = r(. Combining all this yields
(1)This is one form of the Euler turbine equation or simply the Euler equation.
Degree of Reaction The relative proportions of energy transfer obtained by change of both static and dynamic pressures are important factors with respect to classifying turbomachines, as for a given class of machine this proportion inevitably leads to a particular type of design with certain inherent characteristics. The parameter used to describe this relation is the degree of reaction or more simply the reaction, R, which is defined as the ratio of the energy transfer by means of or resulting in a change of static pressure in the rotor to the total energy transfer to (utilized by) the rotor.
( Total energy transferred to the rotor
( linear velocity of the rotor at radius r, = (r
( absolute velocity
( tangential component of absolute velocity
( velocity relative to the moving rotor R, can be negative, zero, and values greater than unity. Reaction TurbinesWater turbines are either reaction turbines or impulse turbines. All common water turbines until the late 19th century were reaction turbines. Reaction turbines are acted on by water, which changes static pressure as it moves through the turbine and gives up its energy. The flow between the rotating vanes of a reaction turbine can be envisioned as flow through rotating nozzles. The pressures within the moving nozzle produce work. The flow must be encased to contain the water pressure (or suction), in order that the fluid cannot expand freely in all directions. Alternately, the vanes must be fully submerged in the water flow as with a ships propeller. Most water turbines in use are reaction turbineseven a simple spinning lawn sprinkler. They are used in low and medium head applications. Two popular types of reaction turbines are the Francis and the Kaplan turbines. In 1826, Benoit Fourneyron developed a high efficiency (80%) outward flow water turbine. Water was directed tangentially through the turbine runner causing it to spin. Jean-Victor Poncelet designed an inward-flow turbine in about 1820 that used the same principles. S. B. Howd obtained a U.S. patent in 1838 for a similar design.
In 1848, James B. Francis improved on the inward-flow design to create a turbine with 90% efficiency. It is also called a radial-flow turbine He applied scientific principles and testing methods to produce the most efficient turbine design ever. More importantly, his mathematical and graphical calculation methods improved the state of the art of turbine design and engineering. His analytical methods allowed confident design of high efficiency turbines to exactly match a sites flow conditions.Francis turbines are the most common water turbine in use today. They operate in a head range of ten meters to several hundred meters and are primarily used for electrical power production.
Figure 1Francis Turbine: (a) Cross section,
(b) Runner used in Grand Coulee DamThe Kaplan turbine is an inward-flow, propeller-type water turbine that has adjustable blades developed in 1913 by the Austrian professor Viktor Kaplan. It was an evolution of the Francis turbine.
Figure 2Kaplan Propeller TurbineIts invention allowed efficient power production in low head applications that was not possible with Francis turbines. Kaplan turbines are now widely used throughout the world in high-flow, low-head power production. Their efficiencies are typically over 90%, but may be lower in very low head applications. Again, most water turbines in use are reaction turbines. They are used in low and medium head applications.Impulse Turbines Zero reaction (R = 0) is an important value and characterizes a particular design of many types of turbomachine. The Knight and Pelton bucket wheels are examples of zero reaction turbines. In 1866, California millwright Samuel Knight invented a machine that worked from a different concept. Inspired by the high pressure jet systems used in hydraulic mining in the gold fields, Knight developed a wheel where the vanes were bucket-like which captured the energy of a free jet, which had converted a high head (hundreds of vertical feet in a pipe or penstock) of water to kinetic energy. This is called an impulse or tangential turbine. The water's velocity, roughly twice the velocity of the bucket periphery, does a U-turn in the bucket and drops out of the runner at low velocity.In 1879, Lester Pelton, experimenting with a Knight Wheel, developed a double-semicylindrical bucket design, which exhausted the water to the side, eliminating some energy loss of the Knight wheel which exhausted some water back against the center of the wheel. In about 1895, William Doble improved on Pelton's half-cylindrical bucket form with an elliptical bucket that