Convergent nozzles

[ATP_Al]

I'm having a systems nightmare!!

Can anyone explain the differences between convergent and convergent-divergent jet pipe nozzles?

Many thanks,

Al

[Keith.Williams.]

A convergent nozzle is one in which the diameter of the outlet is smaller than that of the inlet.

A divergent nozzle is one in which the diameter of the outlet is greater than that of the inlet.

A convergent-divergent nozzle is a convergent nozzle with a divergent nozzle fixed to its oulet.

Jet engines create thrust by accelerating air rearwards. At subsonic speeds airflow passing through a convergent nozzle is accelerated. So for sub-sonic flight a convergent nozzle is used at the outlet of a jet engine exhaust.

The greatest exhaust speed that can be achieved in a convergent nozzle is the local speed of sound (sonic). But to create thrust in supersonic flight the exhaust gas must be accelerated to supersonic speeds.

In order to accelerate sonic airflow to supersonic speeds it must pass through a divergent duct. So supersonic aircraft use convergent-divergent exhaust ducts. The exhaust gas accelerates to sonic speed in the convergent section of the duct then continues to accelerate to supersoinc speeds in the divergent section.

[OneIn60rule]

You beat me to this one! :D

Nice explanation.

[dreamingA380]

http://www.visionengineer.com/aero/nozzle.shtml

Nice simple explanation Keith, See above link for a diagram.

(The only extra clarification I can add, is that in the Con-Di nozzle the exhaust flow is always accelerating.

The acceleration in the convergent part is when the exhaust flow is less than mach 1.

At the narrowest part of the nozzle, the flow is at Mach 1

And at the Divergent part the flow is accelerating beyond Mach 1

Hope all this helps.

[paulfer]

Correct! But don't forget to explain WHY the divergent duct has accellerating air!
Remeber to any student, divergent duct, decellerating air??

[Keith.Williams.]

OK Paulfer, but this may become rather long.

To understand what happens we must go back to PPL level study of duct flows.

The first point to note is that we are talking about steady streamline flow. The ducts have no side passages nor branch lines to allow air to escape from nor come into the system. So whatever mass of air flows into the duct at one end, the same mass must flow out at the other end. This means that the mass flow of air per second at all points in the duct is constant.

The mass of air flowing through any part of the duct during each second is equal to the air density multiplied by the volume of air that flows through that part per second. So to achieve constant mass flow we must have constant volume flow.

The volume of air flowing through any point in the duct is equal to the cross-sectional area of that point, multiplied by the air velocity.

In a convergent duct the cross-sectional area of the inlet is larger than that of the outlet. So the cross-sectional area gradually reduces as the air flows through the duct. This means that to maintain constant volume, flow the velocity of the air must gradually increase to match the gradual reduction in cross-sectional area. So air accelerates as it flows through a convergent duct.

The effect in a divergent duct is exactly the opposite. Aa the cross-sectional area increases, the velocity decreases to maintain constant volume flow.

The second factor to consider is the total energy of the airflow. In a simple duct there is no means of adding energy to the air and (if we ignore friction and conduction of heat through the duct walls) we can assume that no energy is lost from the air. This means that the total energy of the air remains constant. The principal forms of energy possessed by the air are:

Mechanical energy in the form of static pressure.

Kinetic energy (1/2 mV squared) which is evident as dynamic pressure (1/2 Rho V squared).

Thermal energy evident as the temperature of the air.

If velocity changes, then so will the kinetic energy and dynamic pressure. But the total energy in our duct remains constant, so any change in dynamic pressure must be matched by an opposite change in static pressure. So if velocity increases causing dynamic pressure to increase, the static pressure and temperature must decrease. Bernouli described this effect by stating that the total pressure (static plus dynamic) is constant at all points in a stream tube.

The above effects are all described in classical PPL- level study of duct flows. Convergent duct = velocity increase, static pressure decrease and temperature decrease. Divergent duct = Velocity decrease, static pressure increase and temperature increase.

But the above description is based upon the assumption that air density remains constant at all points in the duct. In reality, as velocity increases, the decreasing static pressure allows the air to expand. So as air accelerates through a convergent duct its volume gets bigger.

The volume increase is caused by the static pressure decrease, which is itself caused by the dynamic pressure increase. So if we sketch the way in which dynamic pressure increases with increasing velocity we will also have sketched how the volume increases.

Dynamic pressure is 1/2 Rho V squared, so it increases with the square of velocity. If we sketch a graph of dynamic pressure against velocity we will find that the curve is very flat at low velocities but becomces increasing steep as velocity increases. So for any given velocity increase at low velocities the increase in dynamic pressure ( and hence volume) will be very small. But at high velocities the curve is much steeper, so for the same increase in velocity we will get a much greater increase in volume.
This means that the rate of expansion of the air increases as velocity increases. The remainder of this explanation can best be understood by first sketching the above curve and marking of the velocity axis in 50 ft/sec increments.

We can examine the consequences of all of this by imagining that we are conducting an experiment using a duct in which we can vary the size of the outlet. In our experiment we will provide an airflow at the inlet at a suitable velocity and vary the outlet size so that we always get the same overall increase in velocity. Let's say that we want an increase or 50 ft/sec.

We start with and inlet velocity of 50 ft/sec and adjust the outlet to give us a 50 ft/sec increase so that the outlet velocity is 100 ft/sec. At these speeds the changes in static pressure are very small so they cause only very small cahnges in the volume of the air. These changes are so small that we can ignore them and pretend that the density is constant.

We now increase the inlet velocity to 100 ft/sec, measure the outlet velocity and adjust the outlet size to get our required 50 ft/sec acceleration, and 150 ft/sec outlet velocity. The changes in air volume are still very small so we can again ignore any changes in density. This means that little or no adjustment of the outlet size will have been required.

If we keep repeating this process we will find that the air volume is increasing at an increasing rate. Each stage of the experiment will require a slightly greater outlet size to give us the required 50 ft/sec acceleration.

We will eventually find that the duct is parallel. This is a particularly curious effect, so let's ignore it for now and come back to it later.

When we increase the inlet velocity for the next stage in our experiment we will once again need to open the dutlet to get our required 50 ft/sec acceleration. We now have air accelerating through a divergent duct.

At this stage it is tempting to conclude that Bernouli had it all wrong and all duct flow theory is rubbish. This is not the case. The problem is that we all start our studies by looking only at low speed airflows. At these speeds the changes in volume are so small that we can ignore them. This unfortunately leads most PPL instructors to forget to mention them at all.

But at higher speeds the changes in volume become so large that they can no longer be ingnored. The air is exapanding faster than it is accelerating. So we must open out our duct to enable it to flow through at a constant mass flow rate.

The overall effect of these factors is that at subsonic speeds air accelerates through convergent ducts and decelerates through divergent ducts. But at supersonic speeds the opposite is true. Convergent ducts decelerate the air while divergent ducts accelerate it.

Now let's return to the strange case of acceleration through a parllel duct. At first sight this suggests that using a long enough duct will give us airflow at the speed of light. The problem is that this effect is true only for sonic airflow. At this speed the rate of expanison of the air exactly matches the rate of acceleratio. So the duct must be parallel to give constant mass flow rate. But as soon as this air accelerates it becomes supersonic, and so requires a divergent to in order to accelerate. So acceleration through a parallel duct is possible, but only through an infinitely short section of duct.

The above effects are used in the inlets and exhausts of high speed aircraft. They are also one means of explaining concepts such as expansion and compression corners when studying ATPL level POF.

[ATP_Al]

Think I understand that one now! Thanks to Keith for the explanation, and to the CAA for not asking a question on it this month! ;)

Al