# Changes in the conditions of state of the gas

The **quasi stationary** changes in the conditions of state of the gas when flowing through a compressor stage can be represented in a T,s- diagram.Such a compressor stage can be either part of a multistage or a single stage compressor.

Gas enters the cylinder from the suction chamber in the condition S. During the flow into the cylinder throttling and heating up of the gas occurs.

The **non stationary** change of state in the **working chamber** is limited by points 1 and 2 of condition of state at the beginning and at the end of compression. For the quasi stationary evaluation of the stage the mean pressures during the intake and discharge are relevant.

The **outflow of gas out** of the working chamber is combined with a pressure loss and a cooling of the gas down to the conditions of the receiver D on the delivery side.

With the gas flowing through the **interstage system** its temperature will be reduced to the suction temperature T **s****+** of the next stage. The pressure is reduced due to friction losses to p**s****+****. **( The index + symbolises the next stage ).

For the function of the stage the pressure ratios below are characteristic. (All pressure ratios correlate to a line in the T,s ? diagram.)

According to the first law of thermodynamics the specific work put into a stage equals the heat removed from the working chamber and the interstage system plus the mostly relatively small change in enthalpy of that stage.

# Transport of liquid and liquid separation

Usually the gas contains a certain amount of water vapour, in the extreme case it can be saturated with water vapour. For the **absolute humidity** ( mass ratio of water vapour to dry gas ) there exists a limit , which is proportional to the ratio of vapour generation pressure and the pressure of the gas.

The temperature and thereby the pressure at which vapour is generated at the inlet of subsequent stages only differ slightly .Therefore , with rising pressure of the gas from stage to stage its capacity for holding water vapour is reduced and **partly condensation** occurs. The condensate in the form of droplets has to be removed, as accumulation of water could lead to damage in the next compressor stage ( water hammer, corrosion ).

The **oil** **content** of the gas behind a lubricated compressor stage lies in the range of 10 mg oil / kg gas. The diameter of the droplets is 0,1 to 10 & # 956;m ( most frequent occurrence at approx. 1 μ,m ). These droplets result from being carried away from the oil film on the walls of the intercooler system by the gas flow. Also the oil should be separated behind each stage.

( Designs and application areas of separators )

# Non stationary flow and Gaspulsations

The flow of gas though the interstage systems is only stationary under ideal conditions. In the real compressor the flow can not be stationary.The periodic load cycle in the working chambers result in changing flow velocities and causes therefore periodic **quasi stationary pressure** **changes **in the interstage** **system. These pressure changes are the smaller, the smaller the flow difference at inlet and outlet and the larger the volume of the interstage system.

Each component of a compressor unit where gas flows through it constitutes an **oscillating mass-spring system**, as the component contains a gas mass with an inner elasticity (compressibility ). The simplest shape of such a system is a straight tube. In a tube the gas can carry out longitudinal oscillations. Thereby the basic constant velocity of the gas is superimposed by periodic velocity oscillations . Due to the principle of conservation of energy the oscillations of velocity are linked to oscillations of pressure. The total of these non-steady state processes are called **gaspulsations**. The variations of pressure are normally small compared to the level of working pressure of the gas. They propagate with the speed of sound. They are therefore called **acoustic oscillations.**

Gas pulsations in compressor units are **initiated** by the periodic feeding and removing of gas into or out of adjacent working chambers of the compressor cylinder. The pulsations are dampened through friction of the gasflow in the pipes and in all those chambers which influence the flow of gas.

The excitation of gas pulsations in a compressor plant occurs within a frequency spectrum consisting of the rotary frequency or its multiples (**Harmonics).** The level of the excitation of the individual harmonics can be obtained by a Fourier – analysis of the gas inlet and outlet process. Through the installation of sufficiently large pulsation dampeners before and after the working cylinders the generation of gas pulsations can be substantially reduced in all working conditions.

The local and temporary distribution of pressure fluctuations can be seen as the sum total of the fluctuations at all the excitation frequencies. This fact is normally taken into account when carrying out a calculation and an analysis of gas pulsations.(Alternatively to the calculation with the frequency spectrum a more elaborate but more precise method of calculating the pressure pulsations can be carried outin the time domain.)

The gas pulsations also influence the thermodynamic function of the compressor installation, especially on the working valves. The transient forces are excerted by the gas on various components of the compressor installation . These forces are correlated to the gas pulsations and generate **mechanical vibrations**. The thereby created mechanical stresses depend strongly on the support and fastening of the individual components.

A **pulsation analysis** has to be carried out for all compressor installations already in the design stage. Its objective is to plan the layout in such a way, that the pressure pulsations will not endanger the thermodynamic function nor the mechanical strength. The demands on this pulsation analysis are the higher, the larger the compressor installation and the higher the operating pressure (API 618 [6] and table 2 right).

For medium and large size compressor installations the calculation of pressure pulsations and the overall pressure losses has to be carried out with well proven simulation programs for the actual working conditions and for all part systems. These programs are composed of modules and allow a detailed simulation of the installation. For large installations an analysis of the mechanical vibrations of all components has to be carried out. Also, the influence of the gas pulsations on the operation of the compressor – and especially on the operation of the compressor valves – has to be checked.

The pulsation analysis has to be carried out for all load conditions and for all compositions of the gas. Subsequently an analysis of the mechanical reaction of the various installation components has to be carried out for the operating condition with the largest pressure pulsations. If allowable limits are exceeded, changes on the layout have to take place.

The fitting of throttles at appropriate places in the installation shifts the natural frequencies but increases the pressure loss ∆p and thereby the energy costs of the installation. The use of supports with better friction dampening are more expensive, but avoids additional energy costs [22]. For the specific abatement of defined pulsation frequencies pulsation dampeners of the resonator principle may find application.