TURBOMACHINES

VIJAYAVITHAL BONGALEAssociate Professor and Head

Department of Mechanical EngineeringMalnad College of Engineering,

Hassan – 573 201.Mobile No:9448821954

E-mail : vvb@mcehassan.ac.in 1

APPLICATIONS OF FIRST AND SECOND LAW OF THERMODYNAMICS TO TURBO MACHINES

Properties of the flowing fluid:Fluid at rest: pressure, temperature and volume all directly measurable.Moving fluid: measuring devices used to measure the properties can give different readings depending on the speed and the measuring conditions.1.Turbomachines involves high speed flow2.In a high speed flow two kinds of states are defined a. Static state b. Total or stagnation state

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STATIC STATE:

Pressure, temperature and volume are determined at any given fluid particle and these define the static state of the fluid and the properties are called static properties.

The static properties are measured with instruments which are at rest relative to the fluid.

Example:

To measure the temperature of the fluid moving with a given speed, the measuring thermometer should theoretically move with the same speed as the fluid particle itself while the measurement is being made.

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STAGNATION OR TOTAL STATE:

It is defined as the terminal state of a fictitious, isentropic and work-free thermodynamic process, during which the macroscopic kinetic and potential energies of the fluid particle are reduced to zero in steady flow.

The properties measured at stagnation state are called total or stagnation properties

The initial state for the fictitious process is static state.

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Stagnation versus Static Properties:

Static Properties: Still air•represent the properties you would measure if you were moving with the flow (at the local flow velocity)•always defined in the flow’s reference frameStagnation Properties: Moving air•always defined by conditions at a point•represent the (static) properties you’d measure if you first brought the fluid at that point to a stop (isentropically) with respect to a chosen observer•depends on observer’s reference frame

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STATIC PROPERTIES:

Pressure - P or p , Temperature – T , Specific enthalpy – h, Density – ρ etc.

STAGNATION PROPERTIES:

Pressure – P0 , Temperature – T0 , Enthalpy – h0, Density – ρ0 etc.

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Application of the FIRST law of thermodynamics:

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From equation (3) we conclude that, the energy transfer as work per unit mass flow is therefore numerically equal to the change in stagnation enthalpy of the fluid between the turbomachine inlet and exit.

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Application of the SECOND law of thermodynamics:

• In any turbomachine the energy transfer between the fluid and the blades can occur only by dynamic action

• Work is done when the fluid flows over rotor blades and not over the stator blades

Points 1 and 2 represent the inlet and exit of the stator bladesPoints 3 and 4 represent the inlet and exit of the rotor blades

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For flow between 1 and 2 ideally, there should be no stagnation enthalpy changes, thus h01

= h02

For flow between 3 and 4 however, the stagnation enthalpy change may be positive or negative depending upon whether the machine is power absorbing or power generating.

If the machine absorbs power, h04 > h03 and

if the machine generates power h04 < h03

If the system is perfectly reversible and isentropic, with no energy transfer as work, no changes can occur in 1. stagnation enthalpy 2. stagnation pressure and 3. stagnation temperature between the inlet and outlet of the machine

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In any turbomachine there will be necessarily be a. energy transfer as work and b. Frictional and other losses.

The effect of these losses is to

1.Reduce the stagnation pressure and increase the entropy2.Reduce the net work output in a power generating machine and increase the net work input in a power absorbing machine

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EFFICIENCIES:

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Mechanical losses in turbomachines are very very small, and If mechanical efficiency of all the turbomachines are assumed to be unity, then

ɳPG= ɳ a and ɳPA= ɳ a

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To determine adiabatic efficiency it is necessary to specify the ideal work input or output from the fluid states at the inlet and outlet respectively

The actual work input or output w is the quantity given by,For power absorbing machines, w = h02 – h01 , whereas for power generating machine it is w = h01 – h02

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The ideal work input or output can be calculated by any one of the following four equations:

1.On Total to Total basis w t-t = h02’ – h01 -- for PA = h01 – h02’ -- for PG

2. On Total to Static basis w t-s = h2’ – h01 -- for PA = h01 – h2’ -- for PG

3. On Static to Total basis w s-t = h02’ – h1 -- for PA = h1 – h02’ -- for PG

4. On Static to Static basis w s-s = h2’ – h1 -- for PA = h1 – h2’ -- for PG

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Based on the calculations of mechanical work presented the following efficiencies may be defined:

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