One Dimensional Flow in Axial

Compressors

The flow through axial compressor is essentially three

dimensional as flow properties and velocities are function of r, ? and z. in this module, the flow is assumed to be one

dimensional to avoid the complicated flow analysis which require great effort

for analyzing.

The flow properties and velocities are assumed to vary in

the z direction (i.e. meridional planes) in axial compressors. A meridional

plane is any plane passing by the axis of rotation of the machine. Meridional

for is a two-dimensional flow based on the assumption of asymmetry of flow and

infinite number of stator and rotor blades. The flow properties are assumed to

be constant in r direction. DR.GALAL BOOK

A s we have discussed before the Stage of compressor consist

of a work transfer component with negative work, a decelerating stator and

sometime an accelerating stator may precede the rotor (inlet guide vanes).

photo of 3 component of stages 0 1 2 3

Blade to Blade Flow Path

The velocity components

of the working fluid can

be expressed in three velocity vectors, absolute, radial and relative velocity.

Assuming the radial velocity equal zero. The air approaches the rotor with an

absolute velocity C1 at an angle ?1 from the axial direction. Combining

the absolute velocity vectorially with the blade speed U gives the relative velocity W1 at an angle ?1. After passing through the

rotor, which increases the absolute velocity of the air, the fluid leaves the

rotor with a relative velocity W2 at an angle ?2 determined by the blade outlet

angle. The fluid leaving the rotor is consequently the air entering the stator

where a similar change in velocity will occur. Here the relative velocity W2

will be diffused and leaving the stator with a velocity C3 at

an angle ?3.

The velocity vectors and associated velocity diagram for a

typical stage are shown in Fig {number }

Saravanamutto, HIH,

Rogers, GFC och Cohen, H. Gas Turbine Theory Fifth Edition, Pearson Prentice Hall, 2001.

From Euler turbine equation and Referring to the

velocity triangle in the figure it’s easy to get:

Combining the Euler equation with 1st law

of thermodynamics

We got:

The term I is therefore a constant for the rotor and

is known as the relative total enthalpy.

The flow is assumed

adiabatic and there is no work transfer in the stator, then the total enthalpy

is constant.

In the Figure 7.3 the

thermodynamic states are displayed on the T-S diagram. The distances that

represent the absolute and relative kinetic energies are also shown. The relative

stagnation enthalpy across the rotor remains constant. In the rotor rothalpy

has properties analogous to stagnation enthalpy in the stator. KORPELLA

Stage Efficiency

Is the ratio between isentropic work of compressor to

actual work of compressor

Degree of reaction

Is a measure of the enthalpy rise in the rotor to the

total enthalpy rise in the stage. The degree of reaction R indicates the

portion of energy transferred in the rotor blading. It may be defined based on

the actual enthalpy rise or the isentropic enthalpy rise.

or

Although that there are some differences in the

mentioned expressions of the degree of reaction, but all of them give the same

concept. It’s an important parameter especially for axial machines which defines

the class of machine with particular characteristics, since it’s fixed, the

shape of velocity diagrams and blade arrangement are also fixed. For axial

compressor the degree of reaction is usually 0.5 or higher as the flow is

decelerated through compressor hence high flow turning can’t be carried out. To

increase energy transfer across the stage an increase in rotational speed of

compressor is required.