## Monday, December 12, 2011

### THE RELATIONS BETWEEN PRESSURE, VOLUME AND TEMPERATURE

THE RELATIONS BETWEEN PRESSURE, VOLUME AND TEMPERATURE
 Fig. 2-3 An airflow through divergent and convergent ducts.
7. During the working cycle of the turbine engine, the airflow or ’working fluid’ receives and gives up heat, so producing changes in its pressure, volume and temperature. These changes as they occur are closely related, for they follow a common principle that is embodied in a combination of the laws of Boyle and Charles. Briefly, this means that the product of the pressure and the volume of the air at the various stages in the working cycle is proportional to the absolute temperature of the air at those stages. This relationship applies for whatever means are used to change the state of the air. For example, whether energy is added by combustion or by compression, or is extracted by the turbine, the heat change is directly proportional to the work added or taken from the gas.

 Fig. 2-4 Supersonic airflow through a convergent-divergent nozzle or venturi.
8. There are three main conditions in the engine working cycle during which these changes occur. During compression, when work is done to increase the pressure and decrease the volume of the air, there is a corresponding rise in the temperature. During combustion, when fuel is added to the air and burnt to increase the temperature, there is a corresponding increase in volume whilst the pressure remains almost constant. During expansion, when work is taken from the gas stream by the turbine assembly, there is a decrease in temperature and pressure with a corresponding increase in volume.
9. Changes in the temperature and pressure of the air can be traced through an engine by using the airflow diagram in fig. 2-5. With the airflow being continuous, volume changes are shown up as changes in velocity.
10. The efficiency with which these changes are made will determine to what extent the desired relations between the pressure, volume and temperature are attained. For the more efficient the compressor, the higher the pressure generated for a given work input; that is, for a given temperature rise of the air. Conversely, the more efficiently the turbineuses the expanding gas, the greater the output of work for a given pressure drop in the gas.
11. When the air is compressed or expanded at 100 per cent efficiency, the process is said to beadiabatic. Since such a change means there is no energy losses in the process, either by friction, conduction or turbulence, it is obviously impossible to achieve in practice; 90 per cent is a good adiabatic efficiency for the compressor and turbine.

CHANGES IN VELOCITY AND PRESSURE
12. During the passage of the air through the engine, aerodynamic and energy requirements demand changes in its velocity and pressure. For instance: during compression, a rise in the pressure of the air is required and not an increase in its velocity. After the air has been heated and its internal energy increased by combustion, an increase in the velocity of the gases is necessary to force the turbine to rotate. At the propelling nozzle a high exit velocity is required, for it is the change in the momentum of the air that provides the thrust on the aircraft. Local decelerations of airflow are also required, as for instance, in the combustion chambers to provide a low velocity zone for the flame to burn.
13. These various changes are effected by means of the size and shape of the ducts through which the air passes on its way through the engine. Where a conversion from velocity (kinetic) energy to pressure is required, the passages are divergent in shape. Conversely, where it is required to convert the energy stored in the combustion gases to velocity energy, a convergent passage or nozzle (fig. 2-3) is used. These shapes apply to the gas turbine engine where the airflow velocity is subsonic or sonic, i.e. at the local speed of sound. Where supersonic speeds are encountered, such as in the propelling nozzle of the rocket, athodyd and some jet engines (Part 6), a convergent-divergent nozzle or venturi (fig. 2-4) is used to obtain the maximum conversion of the energy in the combustion gases to kinetic energy.
14. The design of the passages and nozzles is of great importance, for upon their good design will depend the efficiency with which the energy changes are effected. Any interference with the smooth airflow creates a loss in efficiency and could result in component failure due to vibration caused by eddies or turbulence of the airflow.