Compression and expansion of gas

Engineers want to exercise control over the compression and expansion of gases in the operation of their various machines. By implication there must be uncontrolled expansions and it is pertinent to look at those first.

 

I think that these are explosions. So what is an explosion? I can think of only two ways that an explosion of a gas might occur. The first is when a quantity of gas is held in a pressure vessel. We store compressed gas in reservoirs like the air receiver for an air compressor or the tanks used in diving or in medical equipment. If any one of these fails the result is a sudden increase in volume of the gas. The gas produces complex and quite unpredictable results as it pushes things, including other gas, out of its way. It is not a process that offers many opportunities to the mechanical engineer. The second is a chemical explosion. It is possible to mix chemicals to produce a solid or a liquid that contains a fuel and an oxidant that could burn very rapidly indeed if ignited but can be handled quite safely provided that it is not ignited. One such might be an explosive but it might also be a rocket fuel. It depends whether the burning is uncontrolled or controlled. What I have just called burning is in fact the conversion of chemicals from a solid or liquid form that occupies a small volume, to gas with a high concentration of internal energy at high temperature. The burning may take place very quickly and lead to an uncontrolled expansion of gas but it can take place at a steady rate as in a diesel engine, a gas turbine engine, a rocket motor or even on a gas-fired cooking stove. This chapter is not about explosions. It is about the uses of gas where there is flow either at a steady rate or at a controlled rate.

 

It seems to me that there are two devices that mark the extremes of the way we employ gases in engineering. They are the gun and the rocket.

 

In a gun a pipe that is called the barrel is closed at one end and open at the other. A charge of explosive is fitted into the closed end as in figure 13-1 and the round (a bullet or a shell) that fits snugly in the barrel is placed against the charge. If the barrel is secured in some way so that it cannot move, ignition of the explosive charge will create a quantity of gas at high temperature with high internal energy and high pressure that will exert a large force on the round and an equally-large, axial force on the barrel. That force will cause the round to accelerate along the barrel and, as it moves, let the gas expand, accelerating the mass centre of the gas as well. All the time that the round is in the barrel the gas will act on it to increase its speed but at the instant that the round leaves the barrel the gas will expand sideways and have no further effect on the round. The internal energy of the released gas will be dissipated in the air surrounding the gun.

 

Now we must think about this gun from an engineering point of view. The object of a gun is to make the round leave the barrel with as high a speed as possible so work done by the gas on the round whilst the round is in the barrel is “useful” work and the work done by the gas on its own mass centre is not useful. However we know that the mass of the gas is small when compared with that of the round and, at worst, the speed of the mass centre of the gas can only be ½ that of the round so most of the work done by the gas is useful. Once the round leaves the barrel, whatever work the gas may still have been able to do is lost.

 

Figure 13-2 shows the elements of a booster rocket. It is just a very large firework that has been engineered. The booster rocket comprises a casing that is filled with solid propellant fuel mixed with its oxidant to support combustion and a retardant to control the rate at which the fuel burns. At one end of the casing there is a convergent-divergent nozzle of a size commensurate with the thrust required from the booster. The combustion starts in the region of the nozzle and progresses through the fuel and I have shown the fuel partly burnt and combustion about half way up the casing. The combustion produces gas at high pressure and high temperature, so high in fact that it is luminous and one might call it a flame even though it is not burning. That gas flows through the nozzle to produce a high-speed jet and, in doing so creates a force on the booster. It seems that the whole function of the booster is to produce this jet of gas but in fact its function is to produce a force. It is an object of this chapter to find out how this force is created and where it acts.

For now all we need to note is that the function of this booster is to give the gas kinetic energy and this process is now useful where in the gun it was useless.

 

I now have two extremes of the gun where the expansion is resisted by the mass of the round as it undergoes its acceleration and the rocket where the expansion is resisted by the gas in the stream ahead of it also undergoing acceleration. All our practical expansions must lie between these two.

 

In the gun the process lasts only as long as it takes for the round to leave the barrel. In the booster rocket the process of burning produces a steady supply of gas inside the casing and a steady flow though the nozzle until all the fuel is burnt. This chapter is about steady continuous processes and not about flows of short duration.

 

However there is still one more complication in this business of flowing gas. During the expansion in either device there may be eddying, shearing and so on within the gas, so the flow will not be orderly. In this disorder some of the potential to do work that is inherent in the structure of the gas will be lost into its own internal energy and to this extent the expansion is not resisted by forces having direction and therefore capable of doing mechanical work.

 

As a result thermodynamicists talk of fully-resisted, un-resisted and partially-resisted processes whether of expansion or compression and I shall use these terms as well. They also find application in mechanical devices.

 

As this text is about engineering and not physics or mathematics and I think that it is worth stopping to think about the four-stroke engine just to see how gas can and must behave and in doing so set some benchmarks to our mental image of the behaviour of gases. The four-stroke cycle takes place in the cylinders of a reciprocating engine. When the piston in one of the cylinders goes down air is drawn into the cylinder and then the inlet valve is closed so that when the piston makes its upward stroke the air is compressed. Fuel is then injected and ignited to raise the pressure before the working stroke as the piston goes down again. Then the exhaust valve open and in the fourth stroke the products of combustion are pushed out to the atmosphere and the cycle starts again.

 

I suppose that most readers of this text will use engines that rotate at about 3,000 revs/minute when a cycle takes place in about 0.04 seconds. If this seems to be a short time spare a thought for those who design racing car engines to turn over at 20,000 rev/min when the same cycle must take place in 0.006 seconds. The engines of such cars might have 8 cylinders each with a bore of 90 mm and a stroke of 40 mm. This is grossly over-square, presumably to limit the inertia forces on the slider-crank mechanism and the make space for very large valves. Even so the acceleration of the pistons at the ends of their strokes is about . As we can actually watch racing cars using these engines we must conclude that the air can get into the cylinders in the extraordinarily short time that is available and of course get out. It is possible because gases move under a combination of low mass and, by comparison, high forces resulting from really quite modest pressures, for example, during the induction phase of an engine.

 

We can get a very good idea of the behaviour of gases if we first look at the conveying of gas in a pipe and then at the convergent-divergent nozzle.