turbine lecture 2

Hydraulic Machines

محمد معوض. د.أ

4 October 2012 1Dr M-Moawed

Theories of Turbomachines:Euler Theory (Elementary)The simplified theory is based on the following

assumptions:- The impeller has an infinite number of blades, which

signifies a perfect guidance of fluid, neglectingseparation, circulation and turbulence.

- The fluid leaves the impeller tangentially to theblades.

- In the impeller passages, the fluid velocities atsimilar points on all the flow lines are the same.


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Inlet and exit velocity triangles

Dr M-Moawed

Substituting those values in first equation we find:


Pelton Wheel (Pelton Turbine)

• By definition, the impulse turbine is amachine in which the total drop inpressure of the fluid takes place in one ormore stationary nozzles and there is nochange in the pressure of fluid as it flowsthrough the rotating wheel.


Pelton Wheel (Pelton turbine) This turbine is named after Lester A. Pelton (1829 – 1908) an American

Engineer who developed it in the year 1880. Pelton wheel is a high head turbine. It is used with heads of more than 500

metres. Note : A head is the distance the water falls before it strikes the turbine blades.

74 October 2012 Dr M-Moawed

Pelton Wheel (Pelton turbine)… The flow of water is tangential to

the runner. So it is a tangential flow impulse turbine.

A Pelton’s runner consists of a single wheel mounted on a horizontal shaft.

Water falls towards the turbine through a pipe called penstock and flows through a nozzle.

The high speed jet of water hits the buckets (vanes) on the wheel and causes the wheel to rotate.

A spear rod which has a spear shaped end can be moved by a hand wheel.

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This movement controls the flow of water leaving the nozzle, before it strikes the bucket(vane)


Pelton Wheel (Pelton turbine)…

The bucket or vane is so shaped that when the water strikes, it gets split into two and gives it an impulse force in the centre of the bucket. This bucket is also known as splitter.


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# PELTON WHEEL operates under very high heads (up to 1800 m.) and requires comparatively less quantity of water.# It is a pure impulse turbine in which a jet of fluid delivered is by the nozzle at a high velocity on the buckets.

# These buckets are fixed on the periphery of a circular wheel (also known as runner), which is generally mounted on a horizontal shaft.

The primary feature of the impulse turbine with respect to fluid mechanics is the power production as the jet is deflected by the moving vane(s).


* The impact of water on the bucketscauses the runner to rotate and thus develops mechanical energy.

* The buckets deflect the jet through an angle of about 160 and 165 in the same plane as the jet.

* After doing work on the buckets water is discharged in the tailrace, and the whole energy transfer from nozzle outlet to tailrace takes place at constant pressure.


VELOCITY TRIANGLESThe velocity diagrams for the Pelton

wheel are shown in the follwing Figure


Torque and Power Calculation:From the velocity triangles, it can be seen

that W1 =W2 , this can be easily shown byapplying Bernoulli's equation on relative path.The power as given by :


Substitute the values of CU1 and CU2 in the first equation and differentiate with respect to U to get max. Power :


Thus, the maximum power generated from thePelton wheel equals:


and the corresponding ideal efficiency


Pelton wheel efficiency versus velocity ratio


Nozzle Losses:The flow rate must vary in proportion to the

required power for impulse wheel. This isdone by the size of the jet, with a littlechange in jet velocity as possible. This canbe done by varying the position of theneedle. The velocity of the jet could begiven by the following relation:


At full load, when the nozzle is fullyopened, Cv is about 0.98 - 0.99, asthe needle is moved to decrease thenozzle opening, the Cv coefficientdecreases but it is still above 0.9, asthe following Figure:


Variation of Cv with jet opening


Bucket Losses:


Wheel Diameter:

The ratio D/d varies and there is noupper limit, but usually in practice theratio is varying between 6-12.


Speed Regulation:The speed regulation is done by the needle

displacement. The speed regulation is necessary toprotect the wheel from over speed, which couldcause mechanical damage at part load operation.As impulse wheels are usually installed only in highhead plants, there is necessary a long pipe anddangerous water hammer would result if there werea rapid reduction of velocity within it. To avoid this,a jet deflector is used, as seen in the followingFigure. The deflector deviates the jet at part loadwithin the necessary time to regulate the needleposition to meet the new load requirement.


Speed and power regulation


Efficiency and Coefficients:


** If α =180, the maximum hydraulic efficiency is 100%. In practice, deflection angle is in the order of 160–165.

NEXT SECTION WE WILL DISCOUSS THE:

PELTON WHEEL

(LOSSES AND EFFICIENCIES)


# PELTON WHEEL (LOSSES AND EFFICIENCIES)** The jet efficiency ( ηj) takes care of losses in the nozzle and the mechanical efficiency ( ηm) is meant for the bearing friction and windage losses.** The overall efficiency ( ηo) for large Pelton turbine is about 85–90%. Following efficiency is usually used for Pelton wheel.


The following figure shows the total headline, where the water supply is from a reservoir at a head H1

above the nozzle.


# The frictional head loss, hf, is the loss as the water flows through the pressure tunnel and penstock up to entry to the nozzle.

# Then the transmission efficiency is:


** Nozzle velocity coefficient

** Therefore the nozzle efficiency becomes


Example 1:It is desired to construct a hydraulic turbine for ahydraulic power plant to operate under the followingconditions: discharge Q = 3.5 m3/s of water, the availablenet head = 290 meters, the hydraulic efficiency = 0.8, therotating speed = 300 rpm. A Pelton wheel impulse turbinewas selected with the following specifications: the bucketangle β2 = 160°, the coefficient of velocity for the nozzle is0.98. Determine:(a) The brake horsepower, Pelton wheel diameter (assume

the friction coefficient k = 0.2).(b) The required number of jets, comment if the ratio of jet

diameter to wheel diameter = 1/10, also calculate thehead coefficient φ and the specific speed Ns.


4 October 2012Dr M-Moawed37

Solution:

Velocity triangles of Pelton Wheel

*****************************************THANK YOU

&GOOD LUCK

**************************************** 4 October 201241 Dr M-Moawed

turbine lecture 2

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