Design Analysis of Axial Flow Gas Turbines P M V Subbarao Professor Mechanical Engineering Department A Sustainable Non-Biological Muscle by Sir Charles Parson…..

Compressor – Turbine Rotor

Infrastructure for Realization of Newton's’ Laws Stator Rotor

Classification of Gas Turbines

Impulse-Reaction turbine This utilizes the principle of impulse and reaction. There are a number of rows of moving blades attached to the rotor and and equal number of fixed blades attached to the casing. The fixed blades are set in a reversed manner compared to the moving blades, and act as nozzles. The fixed blade channels are of nozzle shape and there is a some drop in pressure accompanied by an increase in velocity. The fluid then passes over the moving blades and, as in the pure impulse turbine, a force is exerted on the blades by the fluid. There is further drop in pressure as the fluid passes through the moving blades, since moving blade channels are also of nozzle shape. The relative velocity increases in the moving blades.

Velocity triangles for turbine model stage Vr2 Va2 Va1 Velocity triangles for turbine model stage Vr2 Vr3 Va3 Vr2 Va2 Vr3 Va3 Vf Vw

Selection of Blade & Flow Angles The gas is delivered to the wheel at an angle a2 and velocity Va2. The selection of angle a2 is a compromise. An increase in a2, increases the value of useful component (Absolute circumferential Component). This is also called Inlet Whirl Velocity, Vw2 = Va2 sin (a2). An increase in a2, decreases the value of axial component, also called as flow component. This is responsible for definite mass flow rate between to successive blades. Flow component Vf2 = Va2cos(a2) = Vr2 cos(b2). The absolute inlet velocity can be considered as a resultant of blade velocity and inlet relative velocity. The two points of interest are those at the inlet and exit of the blade.

Impulse-Reaction Stage of ATurbine Vr2 Va2 Vr3 Va3 Vf Vw The reaction effect is an addition to impulse effect. The degree of reaction p va vr A Physical Linking of Momentum and Energy transactions

First law for fixed blades: First law for moving blades: 1 3 2 Total enthalpy drop in a stage:

Vr2 should enter at an angle b2, the inlet blade angle. Va2 Vr3 Va3 Vf Vw If the gas is to enter and leave the blades without shock or much losses, then relative velocity should be tangential to the blade inlet tip. Vr2 should enter at an angle b2, the inlet blade angle. Similarly, Vr3 should leave at b3, the exit blade angle. In an impulse reaction blade, Vr3 > Vr2 The flow velocities between two successive blade at inlet and exit are Vf2 & Vf3. The axial (basic useful) components or whirl velocities at inlet and exit are Vw2 & Vw3.

The Driving Force on Wheel Vr2 Va2 Vr3 Va3 Vf Vw Power Output of the blade :

Sequence of Energy Losses Gas Thermal Power Blade kinetic Power Gas kinetic Power Nozzle Losses Stage Losses Moving Blade Losses Isentropic efficiency of Nozzle Blade Friction Factor

Irreversible Adiabatic Flow Through A Turbine Stage : SSSF Ideal work wiso = h01 –h03ss Actual work wact = h01 – h03a Isetropic Efficiency of a stage h s 1 2s 3ss 2a 3a 3s

Stage Loading and Flow Coefficient Stage Loading Coefficient: Ratio of specific stage work output and square of mean rotor speed. Flow Coefficient: Ratio of the axial velocity entering to the mean rotor speed.

Sizing of A Turbine Stage y F

Theoretical Model for Loss Estimation The losses in any blade row will be proportional to the dynamic head or kinetic energy in the row. Define the coefficient fs as the ratio of the shaft work output to the sum of the mean kinetic energies within stator + rotor. For a 50% reaction turbine:

Performance Vs Size of A Turbine y fs = F

Vr2 Va2 Vr3 Va3 Vf Vw

Vr2 Va2 Vr3 Va3 Vf Vw

Selection of Geometrical Parameters b2 90-a2

Selection of Geometrical Parameters / (b2+b2) b2

Selection of Geometrical Parameters L/F=2 L/F=1 L/F=0.5 L/F=0 (b2+b3) b2

Design Algorithm

Design Algorithm

Model turbine instrumentation

Design validation