TurbomachinesMEE 304

Specific work The work capacity of a turbomachine per unit mass rate of

flow of fluid is called the specific work (W) of the turbomachine

It is defined as the difference in the useful energy content per unit mass rate of flow medium between the two ends namely pressure and suction ends of the machine

The useful energy content of the flow medium can be expressed as the sum of pressure, kinetic and gravitational potential energies

When the change in density is negligible,

Units of W are m2/s2 or J/kg Specific work is used as a common term for all types of turbo

machines instead of ‘Head’ or ‘pressure ratio’ Head is commonly used for Pumps and hydraulic turbines Pressure ratio is commonly used for compressors and

steam/gas turbines The above equation cannot be used for compressible flow as

the density is not constant .Since by definition, W is the useful energy, it is the work of a the isentropic process

Energy equation From the first law of thermodynamics we have

For applications in turbomachines, the energy term will include internal energy, gravitational potential energy and kinetic energy.

Change in the energy in a finite process between two states is given by

(1)

Sub. In eqn. (1)

Dividing throughout by mass m,

(2)

(3)

Steady flow energy equation. For study flow work through turbomachines, the work term

includes the shaft work and flow work The SFEE can be written as

Since H = U + pV

In terms of specific quantities

Eqn. (4) & (5) is the SFEE for control volume or open system This can be rewritten for various processes in various

turbomachines and their componentsHydro – Turbomachines Here ρ =1/v = Constant , u1≈ u2 and q ≈ 0 So we have from eqn (5)

(5)

(4)

(6)

Guide blades and draft tubes These are stationary, so shaft work is zero, then eqn. (6)

becomes

Compressible flow machines Most of the compressible flow machines such as gas turbines,

compressors and blowers are adiabatic machines, ie. q = 0 In these machines change in PE also negligible as compared to

others, so the eqn .(5) becomes

The shaft work is given by

If the entry and exit velocities are small or the difference between them is negligible, then the shaft work is given by the difference between the static enthalpies

Stagnation state & Stagnation properties A state defined by the stagnation temperature and pressure is

the “stagnation state” The stagnation state of a gas is often used as a reference state.

Stagnation enthalpy It is defined as the enthalpy of the gas or vapour when it is

adiabatically decelerated to zero velocity

The stagnation enthalpy is constant in a flow process that does not involve a work transfer or a heat transfer even though irreversible processes may be present

The stagnation state is represented by the point 01 brought about by an irreversible deceleration.

For a reversible deceleration the stagnation point would be at point 01s and the state change would be called isentropic.

Stagnation temperature The stagnation temperature is defined through stagnation

enthalpy For a perfect gas we have

and

Where M is the Mach number The mach no. is defined as the ratio of local velocity of the

gas to the local velocity of sound

Stagnation velocity of sound

Since

Stagnation pressure It is the pressure of gas or fluid is obtained by decelerating it

in a reversible adiabatic(isentropic) process The ratio of stagnation and static pressure can be obtained as

follows

When the pressure changes are small, the process can be assumed to be incompressible. Then stagnation pressure can be determined from the Bernoulli eqn.