Analyzing Pelton Turbine for Aircraft Engine Application: Forces

This assignment evaluates the feasibility of utilizing a Pelton turbine design in an aircraft gas turbine engine, contrasting its typical use in hydroelectric power generation with the requirements of aircraft propulsion. It explains why applying a Pelton turbine, which relies on converting the kinetic energy of a water jet, is not suitable for a gas turbine that operates on the Brayton cycle. The analysis emphasizes that the back pressure generated by adding Pelton blades would reduce the engine's efficiency and thrust. Furthermore, the document derives equations for the forces acting on the turbine blades, considering factors such as fluid density, jet velocity, blade velocity, and deviation angle, ultimately determining the net force and work done by the jet stream on the blades.

1) In general, the Pelton turbine designs are used only to convert the kinetic energy possessed by a jet of
water stream into mechanical energy which is further converted into electrical energy with the help of
generator or alternator. In this case, the engineer suggests to utilize the Pelton turbine design in the
aircraft application, an aircraft engine utilizes a gas turbine which runs on a gas cycle also known as
Brayton cycle which is named after the George Brayton who invented it. There are 4 processes in any gas
turbine which follows the Brayton cycle they are intake, compression, Combustion and Exhaust to the
atmosphere. In gas turbine, The gas is sucked in from the atmosphere compressed with the help of
compressor and then it is burnt with the fuel which finally escapes via Nozzle. The nozzle is a critical part
of any engine that runs on the Brayton cycle. The nozzle generates the thrust that is required to propel the
engine forward. So as per the engineer says if we place a Pelton blade at the rear end of the gas turbine
then the back pressure will be reduced which in turn reduces the efficiency of the cycle. The back
pressure generated at the rear end of the nozzle is directly associated with the amount of thrust produced
so if a negative pressure is developed at the end of nozzle it will directly affect the efficiency of the
engine. The peloton turbine is an impulse turbine which is dependent upon the density of the fluid as the
water is denser than the air the striking force is higher. The impulse force of a fluid with higher density is
very much greater than that of the impulse force of a fluid with lower density, as a density of any fluid is
directly related with the impinging mass and velocity. Thus the Pelton turbine is suited well only for the
applications involving water or denser fluid mediums. The efficiency, dependability, cost of operation
and the service life are directly affected thus the idea proposed by the engineer is not a viable one.

2) Forces on the turbine blades:
Fig1. Jetstream impinging on the Pelton bucket.
Now let us solve the forces that are acting on the buckets of the Pelton wheels.
Considering the System as a control volume and applying the moment of energy principle the moment
force imparted by the jet stream is equal to the moment imparted on the blades of the turbine wheel.
Let, H be the net head of fluid acting upon the Pelton wheel
H = Hg-hf
hf is given by
hf = 4 fL V 2
Dp X 2 g
here,
Dp is the dia of the penstock
D is the dia of the Pelton wheel
N is the rpm of wheel

d is the diameter of the impinging jet
Moment, P = Mass X Velocity
Taking unit mass let us calculated the velocities imparted by the stream
Velocity is given as
Vn = √2 gH ………………………….equation 1
Here,
Vn is the normal velocity
g is the acceleration due to gravity
H is the total head
u is the speed of the wheel in rpm
u = u1 = u2 = πDN
60 ………………………………equation 2
The velocity triangle at the inlet is a straight line with a velocity of Vb
Vb = Vn – u1
Vw= = Vn when (α = 0 and ϴ = 0)
Now let us calculate for the outer velocity triangle from the given image
We have,
Vb1 = Vb2 and Vw2 =Vb2 Cos ө – u2
Now the total force exerted on the wheel by the jet is given by,

Fx = ρ a V n [V w 1−V w 2 ]
Here,
The Fx is the total force acting on the turbine wheel
ρ is the density of the fluid.
Vn is the initial velocity.
Vw is the whirl velocity.
a is Area
The area is given by, a = π
4 d2
Here,
d is the diameter of the penstock.
Now we have derived the net force acting on the turbine wheel now let us derive the net work done by
the jet stream on the blades of the runner per seconds.
NetWork done by the stream of a jet on the blades of the runner per second = Fx (u)
Work done, W = (ρ a V n [ V w 1−V w 2 ]) (u) Watts
Thus the force exerted on the Pelton turbine and the work done per second are derived.