Unit 3

Unit 3

Compressors & combustion chambers

Introduction to Compressors

A compressor is a mechanical device that increases the pressure of a air by reducing its volume. Compressors are work absorbing devices which are used for increasing pressure of fluid at the expense or work done on fluid.

The compressors used for compressing air are called air compressors. Work required for increasing pressure of air is available from the prime mover driving the compressor.

Generally, electric motor, internal combustion engine or steam engine, turbine etc. are used as prime movers. Compressors are similar to fans and blowers but differ in terms of pressure ratios. Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe.

Compressor

Compressed air is a air which is kept under a certain pressure, usually greater than that of the atmosphere.

Compressed air can be used in or for:

pneumatics, the use of pressurized air to do work.

Air dusters for cleaning electronic components that cannot be cleaned with water.

railway braking systems

road vehicle braking systems.

Types of compressors

compressor work on two principles

1)Reduce volume of a constant amount of air 2)Adding more gas/air in a constant amount of volume .

positive displacement compressor works on first principle it reduces the volume of air by applying force on it but air amount is constant in every stroke or rotation thus increasing the pressure.

centrifugal & axial flow compressor works on second principle it adds more amount of air in a given constant volume thus the pressure increase.

The basic requirement of compressor for aircraft gas turbine application are well known.

1.High air flow capacity per unit frontal area

2.High pressure ratio per stage.

3.High efficiency.

4.Discharge direction suitable for multistaging.

The compressor should be designed in such a way to have

1.Minimum length

2.Weight must be as low as possible.

3.The mechanical design should be simple , so as to reduce manufacturing time and cost.

4.High reliability.

Axial flow Compressor History

The basic concept of multistage axial flow compressor operation have been known for approximately 100 years being presented to French academic des science in 1853.

Efficiencies for this type of unit were quite low. Because the blading was not designed for the condition of a pressure rise in the direction of flow.

Beginning of at the turn of 20th century, a number of axial flow compressors were built , in some cases with the blade design based on propeller theory.

The efficiency of these units was still low (50-60%).Due to lack of sufficient knowledge of fluid mechanics at that time.

The advances in aviation during the period of WW I and rapidly developing background in fluid mechanics and aerodynamics give a new impetus to research on compressors.

Axial flow Compressor History

In 1936 the Royal aircraft establishment in England began the development of axial flow compressors for jet propulsion.

Aerodynamic theory was developed specifically for the case of a cascade airfoils.

By 1945 , compressors of high efficiency could be developed by incorporating aerodynamic principles in design and development.

Geometry and Working principle

The energy level of air or gas flowing through it , is increased by the action of the rotor blades which exert a torque on the fluid.

This torque is supplied by an external source an electric motor or gas turbine.

Its applications in the industrial gas turbine units the multistage axial compressor is the principle element of all gas-turbine power plants for land and aeronautical application.

Axial Flow Compressor

An axial flow compressors are given more preferred then the radial flow type in the applications of aircraft and industrial gas turbines . Because axial flow compressor has high efficiency and is capable of producing higher pressure ratio on single shaft.

The stage pressure ratios of about 1.15:1 are obtained and by combining the stages , the overall pressure ratios of upto 8:1 or even higher can be achieved.

The axial flow compressors consists of a number of stages where each stage may be considered as a fan.

The main advantage of axial flow compressors are large air handling abilities with a small frontal area ,a straight through flow systems and high pressure ratios with relatively high efficiencies.

The main disadvantages is its complexity and cost.

Axial flow compressors

An axial flow compressors is composed of an alternating sequence of fixed and movable sets of blades.

The set of fixed blades are spaced around the inside periphery of an outer stationary casing, and together constitute stator.

The set of movable blades are fixed to a spindle and the combination constitutes the rotor.

The radius of rotor hub and the length of the rotor blades are designed so that there is only a very small tip clearance at the end of the stator and rotor blade.

The rotor and stator banks are as close as possible for efficient flow.

One set of stator blades and one set of rotor blades constitute a stage.

There are number of stages in compressors depending upon the pressure ratio required.

The successive set of blades are reduced in length to compensate for the reduction in volume resulting from the increased pressure.

Axial flow compressors

The K.E is imparted to the air by means of the rotating blades which is converted into a pressure rise.

The air enters axially in to the inlet guide vanes where it is turned through a certain angle to impinge on the first row of rotating blades with proper angle of attack.

The rotating guide vanes add K.E. to the air. Here slight pressure rise also takes place. The air then is discharged at the proper angle to the first row of stator blades where the pressure is further increased by diffusion.

The air then directed to second row of moving blades and the process is repeated through the remaining stages of the compressors.

Usually at entry one more stator is provided to guide the air correctly into the first rotor. This blades are some times referred as the Inlet Guide Vanes(IGV).

In many compressors there are one to three rows of diffuser or straightener blades installed after the last stage to straighten and slow down the air before it enters into the combustion chamber.

Axial flow compressors

Axial flow compressors

Selection of Pressure Ratio per Stage

Stage velocity triangle

The flow geometry at the entry and exit of the compressor stage is described by the velocity triangles at these stations .

The velocity triangles for the compressor stage contain, besides peripheral velocity(u) of the rotor blades both the absolute(c) and relative (w)fluid velocity vectors.

These velocities are related by the following vector equation

c = u + w (vector)

Velocity triangles are typically used to relate the flow properties and blade design parameters in therelative frame(rotating with the moving blades), to the properties in the stationary or absolute frame.

Velocity triangle

The air angles of absolute and relative systems are denoted by 1, 2, 3 and 1, 2, 3, respectively.

If the flow is repeated in another stage then

c1 = c3 and 1 = 3

subscripts a and t denote axial and tangential directions respectively.

Thus the absolute swirl or whirl vectors ct1 and ct2 are the tangential components of absolute velocities c1 and c2 respectively .

similarly wt1 & wt2 are the tangential components of the relative velocities w1 & w2 respectively.

The following trigonometrical relations obtained from velocity triangles.

From velocity triangles at the entry:

ca1 = c1 cos1 = w1 cos1 ------------------------------------1

ct1 = c1 sin1 = ca1 tan1 ------------------------------------2

wt1 = w1 sin1 = ca1 tan1 ------------------------------------3

u = ct1 + wt1 -----------------------------------4

u = c1 sin1 + w1 sin1 -----------------------------------5

u = ca1 ( tan1 + tan1 ) ------------------------------------6

From velocity triangles at the exit:

ca2 = c2 cos2 = w2 cos2 ------------------------------------7

ct2 = c2 sin2 = ca2 tan2 ------------------------------------8

wt2 = w2 sin2 = ca2 tan2 ------------------------------------9

u = ct2 + wt2 ------------------------------------10

u = c2 sin2 + w2 sin2 -----------------------------------11

u = ca2 ( tan2 + tan2 ) ------------------------------------12

for constant axial velocity through the stage:

ca1 = ca2 = ca3 = ca ------------------------------------13

ca = c1 cos1 = w1 cos1

= c2 cos2 = w2 cos2 ------------------------------------14

Equation 6 &12

u/ ca = 1/ = ( tan1 + tan1 ) = ( tan2 + tan2 ) ------15

This relation can also be presented in another form using eqn 4 & 10

ct1 + wt1 = ct2 + wt2

ct2 - ct1 = wt1 - wt2 -----------------------------------16

ca ( tan2 - tan1 ) = ca ( tan1 - tan2 )----------17

Equations 16 & 17 give the change in the swirl components across the rotor blade row .For steady flow in an axial machine, this is proportional to the torque exerted on the fluid by the rotor.

Work input to the compressor

Compressor work input in terms of velocity and blade angles . The compressor work input derived based on the assumption that the axial velocity remains constant throughout the machine.

From eqn 15

u = ca( tan1 + tan1 ) = ca( tan2 + tan2 )

Form Eulers eqn for turbo machinery the power needed by rotor is

P = M = (ct2r2 - ct1r1) where = u1/r1 = u2/r2

Above eqn becomes

P = (ct2u2 - ct1u1)

Dividing above eqn by we will get workdone or specific power

W = u(ct2-ct1)

W= u ca( tan2 - tan1 )

In terms of

W = uca ( tan1 - tan2 )

Variation occurs in axial flow compressors

Absolute velocity , cRelative velocity , wFlow widthStatic pressure , PTotal pressure, PoRotor Increase Decrease Increase Increase Increase statorDecrease -Increase Increase Constant

According to Eulers (turbo machinery) energy equation

W = {(c22 c12)+(u22 u12)+(w12 - w22)}

For axial flow compressors u=u1=u2 the above equation reduced to

W = 1/2(c22-c12)+1/2(w12-w22)

To obtain higher efficiency the work input should be as minimum as possible . To achieve this , the proper care in the design of blade and flow geometries are essential.

Work done factor()

The reduction in work absorbing capacity of the compressor is measured by work done factor(0.98-0.85)

It is a measure of the ratio of the actual work absorbing capacity of the stage to its ideal value as calculated from equation.

W = uca ( tan1 - tan2 )

This work done factor accounts for the effect of boundary layer and tip clearance.

In terms of temperature difference

Ts = T02 - T01

CpTs = uca ( tan1 - tan2 )

Ts = uca ( tan1 - tan2 )

Cp

Compressor stage efficiency

It is the ratio b/w ideal work input to the actual work input.

Wideal = h03 h01

= Cp(T03 T01 )

Wactual = h03 h01

= Cp(T03 T01 )

c = (T03 T01 )

(T03 T01 )

Actual Stage work in terms of velocities and air angles

Wactual = h03 h01 = uca( tan2 - tan1 )

= uca ( tan1 - tan2 )

= 1/2(c22-c12)+1/2(w12-w22)

Performance coefficients

In order to evaluate the performance of the compressor same dimensionless performance coefficients are found useful in various analyses.

1.Flow coefficient

it is defined as the ratio of axial velocity to peripheral speed of the blades. Flow coefficients sometimes called as compressor velocity ratio.

2.Rotor pressure loss coefficient

it is defined as the ratio of the pressure loss in the rotor due to relative motion of air to the pressure equivalent of relative inlet velocity.

3.Rotor enthalpy loss coefficients

it is defined as the ratio of the difference between the actual and isentropic enthalpy to the enthalpy equivalent of the inlet relative velocity.

4.Stator/Diffuser pressure loss coefficient

it is defined as the ratio of the pressure loss in the diffuser due to flow velocity to the pressure equivalent of actual inlet velocity of the diffuser.

5.Stator/Diffuser enthalpy loss coefficient

it is defined as the ratio of the difference between the actual and isentropic enthalpy to the enthalpy equivalent of absolute velocity of flow at diffuser inlet

6.Loading coefficient

it is defined as the actual stagnation enthalpy rise in the stage to enthalpy equivalent of peripheral speed of rotor.

Degree of reaction

The degree of reaction prescribes the distribution of the stage pressure rise b/w the rotor and the stator blade rows.

for an actual compressor stage the degree of reaction is define as (R)

actual change of enthalpy in rotor

actual change of enthalpy in stage

LOW REACTION STAGE:(R ( P)d

Since the rotor blade rows have relatively higher efficiencies , it is advantageous to have a slightly greater pressure rise in them compared to diffuser.

Flow losses

Aerodynamic losses occurring in the most of the turbo machines arise due to the growth of boundary layer and its separation on the blade and passage surface .

Types of aerodynamic losses

1.Profile loss 2.Tip clearance loss 3.Stage loss

Performance characteristics

The performance characteristics of axial flow compressors or their stages at various speeds can be presented in terms of the plots of the following parameters.

1.Presssure rise vs flow rate

2.Pressure ratio vs non-dimensional flow rate

0ff-design operation

The performance of a compressor is defined according to its design. But in actual practice, the operating point of the compressor deviates from the design- point which is known as off-design operation.

Unstable flow in axial compressors can be due to two reasons.

1.Seperation of flow from the blade surfaces called stalling.

2.Complete breakdown of steady through flow called surging.

Compressor surge

It is a form of unstable operation and should be avoided.

Surge has been traditionally defined as the lower limit of stable operation in a compressor, and it involves the reversal of flow.

This reversal of flow occurs because of some kind of aerodynamic instability within the system.

Usually, a part of the compressor is the cause of the aerodynamic instability, although it is possible for the system arrangement to be capable of augmenting this instability.

A decrease in the mass flow rate, an increase in the rotational speed of the blade, or both can cause the compressor to surge.

One should note that operating at higher efficiency implies operation closer to surge.

Surge is a reversal of flow and is a complete breakdown of the continuous steady flow through the whole compressor. It results in mechanical damage to the compressor due to the large fluctuations of flow which results in changes in direction of the thrust forces on the rotor creating damage to the blades.

Compressor Stall

There are three distinct stall phenomena. Rotating stall and individual blade stall are aerodynamic phenomena; stall flutter is an aero elastic phenomenon.

Individual Blade Stall

This type of stall occurs when all the blades around the compressor annulus stall simultaneously without the occurrence

of a stall propagation mechanism.

The circumstances under which individual blade stall is established are unknown at present.

It appears that the stalling of a blade row generally manifests itself in some type of propagating stall and that individual blade stall is an exception.

Rotating Stall

Rotating stall (propagating stall) consists of large stall zones covering several blade passages and propagates in the direction of the rotation and at some fraction of rotor speed. The number of stall zones and the propagating rates vary considerably .

This stalled blade does not produce a sufficient pressure rise to maintain the flow around it, and an effective flow blockage or a zone of reduced flow develops.

Stall Flutter

This phenomenon is caused by self-excitation of the blade and is an aero-elastic phenomenon. Stall flutter is a phenomenon that occurs due to the stalling of the flow around a blade.

Blade stall causes Karman vortices in the airfoil wake. Whenever the frequency of these vortices coincides with the natural frequency of the airfoil, flutter will occur. Stall flutter is a major cause of compressor blade failure.

Effects of stall

This reduces efficiency of the compressor

Forced vibrations in the blades due to passage through stall compartment.

These forced vibrations may match with the natural frequency of the blades causing resonance and hence failure of the blade.

Centrifugal compressors

1.It consists of a rotating element called impeller and a volute casing.

2.The air enters into the compressor through the suction eye of the impeller. Due to the rotation of the impeller at a high speed produces centrifugal force which causes the air to move out of the impeller at a high velocity.

3.Then the air with high velocity enters into a diffuser ring. The diffuser blades of the diffuser ring are so shaped that these provide an increased area of passage to the air which is passing outwards due to which the velocity of air leaving the impeller is reduced and its pressure is increased.

4.The high pressure air then flows to the divergent passage of volute casing. The velocity of air is further reduced due to increased cross sectional area of volute casing causing very small rise in pressure.

5.From the casing the compressed air leads to exit pipe and finally comes out of the compressor.

5.This type of compressor is a continuous flow machine suitable for large flow rate at moderate pressure. The pressure ratios between 4 to 6 may be obtained in this type of compressor. Pressure ratio upto 12 can be obtained by multistage centrifugal compressors.

Types of diffuser

The diffuser consists of any annular space known as a vaneless diffuser.

The diffuser consists of a set of guide vanes it is known as vanned diffuser . The main aim of this diffuser is to increase the static pressure by reducing the kinetic energy.

Pressure rise across compressor

1

2

3

Inlet

Casing

Impeller

Diffuser

P

Channel

0

Ideal energy transfer

Let us first considered the case of an ideal compressor with the following assumptions for radial vaned impeller.

1.Losses due to friction are negligible

2.Energy loss or gain due to heat transfer to or from the gas is considered very small.

3.The gas leaves the impeller with a tangential velocity equal to the impeller velocity , no slip condition is assumed.(ct2=u2)

4.The air enters the rotor directly from the atmosphere without tangential component.ct1= 0

Applying these assumptions to the Euler's energy equation under ideal conditions becomes.

E = ct2u2-ct1u1 (or)

E = {(c22 c12)+(u22 u12)+(w12 - w22)}

E = u22

This is the maximum energy transfer that is possible. therefore the work done by the impeller on unit quantity of air is given by

W = E = u22

Energy transfer equation from thermodynamic analysis

W = E = h02 - h01 = Cp(T02 T01 )= Cp T01(rc(-1/) -1)

u22 = Cp T01(rc(-1/) -1)

Blade shapes and velocity triangles

In order to understand the actual energy transfer and flow through compressor we will use two velocity triangles.

1.Entry velocity triangles

2.Exit velocity triangles

The absolute and relative air angles at entry and exit of the impeller are denoted by 1, 2 and 1, 2.

Based on the value of 2 the blade shapes are given the name as forward curved blades (2>90),Radial blades (2=90),Backward curved blades(2