# Physics behind turbochargers and compressors

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1. Apr 21, 2015

Hi everyone,

I need to do a presentation to a high school class about the physics behind a turbocharger and was looking for some help getting which principals/laws explain what happens when a turbocharger is used within a car i.e.; Thermodynamics, gas laws.

I just need a direction in which to head while researching and compiling a presentation, so topics/resources if possible would be much appreciated.

2. Apr 21, 2015

### SteamKing

Staff Emeritus
You should do the basic research about these devices online. There's plenty of information available out there.

If you have any questions about what you found, you can ask them here.

3. Apr 21, 2015

### billy_joule

Are you in high school yourself?
Presentations need to be aimed at the audience. You need to find out what level the students are at and tailor your presentation to suit.

4. Apr 21, 2015

### jack action

The basic equations are pretty much the usual suspects.

On the compressor side, you use the ideal gas law in its molar form to show that when you increase pressure, density and/or temperature are also increased. You can then used the polytropic process relationship to demonstrate that it will be in fact both density and temperature that will increase. Of course, an increase in density is what you are after to put more air within the cylinder, thus burning more fuel.

On the turbine side, you can use the concept of total enthalpy and temperature to explain the conservation of energy between internal energy and kinetic energy (when speed increases, the temperature drops and vice-versa). I like the idea of comparing it with the Bernoulli principle which basically states the same thing for incompressible flow (again the ideal gas law can help to show the relationship).

Then the polytropic process relationship comes again into play to explain how useful work can be extracted from a turbine by modifying total properties of the exhaust gases.

5. Apr 26, 2015

jack action,

When you say that as the speed increases and the temperature drops, are you referring to the air which is being pulled into the system?

Also, how does the polytropic process demonstrate that both density and temperature will increase?

I have tried my best to understand through wikipedia and some videos but as a high school student they concepts are new to me

Thanks

6. Apr 27, 2015

### jack action

No, I'm talking about the exhaust gas temperature.

The temperature is basically a measure of the energy contained in matter (We call it enthalpy). Every substance has a property called heat capacity (Cp) and the relation between its temperature (T) and its specific enthalpy (h, which is the enthalpy compared to the mass of the substance) is .

When you add motion to this substance, you add kinetic energy that can be recovered if you decelerate it. That is what you do in a turbine. The amount of kinetic energy is ½mv², if you want to compare it with specific enthalpy, you have to divide it by the mass (m), so the specific kinetic energy is ½v². So the total enthalpy in a substance that is in motion is:

If you divide the previous equation by Cp:

T0 is called the total temperature. It represents the temperature that would have the substance if it was decelerated to zero.

Now, when the exhaust gases enter the turbine it has a certain temperature and it goes a certain speed, which means we know its total enthalpy (h0). The turbine will decelerate the flow of exhaust gas and use the removed energy to run the compressor. So its total enthalpy will drop, so will its total temperature. This means that if the exhaust gases were to decelerate by itself, it would have a certain increase in temperature (½v²/Cp). With a turbine, the exit velocity will be smaller, so the temperature increase will also be smaller when at rest.

In summary:
• Temperature is a measure of energy;
• Speed can also be a measure of energy;
• A turbine convert energy into mechanical work;
• Therefore, once some energy is removed, the temperature and/or speed of the exhaust gas have to decrease.

So we know that Pv = RT. Only R is known, so we need another equation to establish a relation between at least 2 of the 3 unknowns (P, v, T). The polytropic process stipulates that Pvn = C or P = C / vn, where C is a constant.

To eliminate C, we imagine a gas that is in 2 different states, 1 and 2, both states having their own properties P,v, and T. So, the polytropic process says that C = P1v1n. But the polytropic process says that C is also equal to P2v2n. So:

P1v1n = P2v2n

Or:

P2 / P1 = v1n / v2n

AS long as n > 0, this proves that if v1 > v2 (or ρ2 > ρ1, according to the definition of specific volume), then P2 > P1 (and vice-versa).

Furthermore, the ideal gas law says:

P2 / P1 = (RT2 / v2) / (RT1 / v1)

or:

P2 / P1 = T2 / T1 * v1 / v2

So the previous relationship can be rewritten as:

T2 / T1 * v1 / v2 = v1n / v2n

or:

T2 / T1 = v1n-1 / v2n-1

Combining the 2 relationships, we can find the following:

T2 / T1 = (P2 / P1)(n-1)/n

Again, as long as n > 1, this proves that if P1 > P2, then T2 > T1.

So both density and temperature are increased when the pressure is increased in a polytropic process when n > 1. In a compressor or turbine, the process is adiabatic (or very close to it), so n is always greater than 1.

Last edited by a moderator: Apr 19, 2017
7. Apr 27, 2015

Jack Action,

Without a turbocharger to increase the volumetric efficiency of an internal combustion engine, how can I explain the effectiveness of inputting of charge into a naturally aspirated engine?

My mind wants to head to the simple direction of, a piston pushes exhaust out during the exhaust stroke and 'sucks in' air during the intake stroke, but the physics here can't be that simple (can it?)

I have thought of the idea of centrifugal inertia (Kadenacy effect) which might occur within the cylinder, which is a result of the pressure differential the exhaust gasses create within the cylinder which may help 'sucks in' air into the cylinder during the intake stroke, but other than the change in pressure the piston makes during the intake stroke, what effects how effectively air is charged into cylinder in a N/A engine?

Through your comments I have gotten a slight grasp around the basic thermodynamic concepts which are present with a compressor/turbine, I just want to further understand the concepts which occur to a naturally aspirated engines that help them move charge in/out of a cylinder.

EDIT: Spelling

Last edited: Apr 27, 2015
8. Apr 27, 2015

### jack action

Yes, it can be that simple. When the piston goes down, it creates a vacuum (i.e. the pressure goes lower than atmospheric pressure) so the air outside the cylinder wants to go in. That pressure differential can be so strong that in early engine designs, there wasn't a cam to open the intake valve, it just opens by itself under that force created by the vacuum (see the first minute of this video). For the exhaust, even if the piston wasn't going up, the pressure inside the cylinder is always higher than atmospheric pressure, so the gases want to get out as soon as the valve opens.

But without proper valve event tuning, the volumetric efficiency is not that good (maybe 70% or so).

The Kadenacy effect is the result of pressure waves going back and forth in the exhaust pipe (it also happens in the intake too). Proper valve event tuning can take advantage of those pressure waves to help fill in the cylinder, if they arrive at the proper time to either suck out exhaust or push in fresh air. With proper exhaust & intake tuning you can easily get 95% volumetric efficiency and values up to 110% can be achieved. I wrote posts in a few threads about the subject, which are summarize in this post.

But all of this has to do with gas dynamics and not thermodynamics, which is another complicated field.

9. Apr 28, 2015

Jack,

How is useful work be extracted from the exhaust gasses? I would imagine through the use of exhaust to spin a turbine, but the website that you directed me to is a little bit strange, is it trying to show the correlation between the work it can produce and the mass of air which is spinning it?

Should it be the work done on the turbine, which I presume is the change in enthalpy from the beginning to the end of the turbine? (ht = h + v^(2) / 2)

Also, does Total Temperature represent the energy the air would have if it had no kinetic energy? So the total amount of energy available to be used to spin the turbine?

Last edited: Apr 28, 2015
10. Apr 28, 2015

### jack action

The exhaust flow has a certain enthalpy before it enters the turbine and another one after it exits the turbine. The difference between the two must be the work done by the turbine:
$$W_{turbine} = h_{in} - h_{out}$$
The enthalpy can be related to the total temperature of the exhaust gases:
$$W_{turbine} = C_p T_{0 in} - C_p T_{0 out}$$
And the temperature ratio can be related to the pressure ratio across the turbine, as I explained in my previous post:
$$\frac{T_{0 out}}{T_{0 in}} = \left(\frac{p_{out}}{p_{in}}\right)^{\frac{n-1}{n}}$$
Using that relation and putting it into the work equation:
$$\begin{eqnarray*} W_{turbine} & = & C_p T_{0 in} - C_p T_{0 out} \\ & = & C_p \left(T_{0 in} - T_{0 out} \right) \\ & = & C_p T_{0 in}\left(1 - \frac{T_{0 out}}{T_{0 in}}\right) \\ & = & C_p T_{0 in}\left( 1 - \left(\frac{p_{out}}{p_{in}}\right)^{\frac{n-1}{n}} \right) \end{eqnarray*}$$
Usually, $p_{out}$ is the atmospheric pressure and all we need to know is the condition at the inlet of the turbine, i.e. the pressure $p_{in}$ , the temperature $T_{in}$ and the velocity $v_{in}$ of the gases (remember that $T_{0 in} = T_{in} + \frac{v_{in}^2}{2C_p}$).

So it really just start with the law of conservation of energy, i.e. the gas flow has some energy coming in, some of it is removed to do useful work for the turbine and the rest goes out the exhaust. The energy is essentially «stored» in 3 forms: compression (pressure), heat (temperature) and motion (velocity).

11. May 3, 2015

Jack,

Thanks for your help, I have made a powerpoint slideshow which basically is outlined like this:

Traditional 4-stroke otto cycle engines use air which is charged at the current ambient air pressure and density, at higher speeds these engines have problems putting charge into the cylinders as the valves are not open long enough for air to efficiently be charged into the cylinder. This partially explains why naturally aspirated engines have problems achieving volumetric efficiency above 100% at higher engine speeds, as being naturally aspirated becomes a bottleneck at higher RPMs.

This leads to the turbocharger, which compresses and pressurizes the air prior to being put into the cylinders, this is known as 'boost'. The turbocharger consists of a compressor wheel and a turbine wheel which both share a common shaft. Exhaust gasses spin the turbine which in return spins the compressor. A blowoff valve and a wastage are two key components which make the current turbocharger design feasible.

The compressor half of the turbocharger's main goal is to increase the density of air which can reach the engine's cylinders, as a result the engine will have more oxygen to be able to produce more effective power through combustion. During compression, the air follow the natural gas law, stating Pv = RT. This shows that as pressure increases through the compressor, the volume of air will decrease (increased density) and the temperature will also increase. Although volume decreases as pressure increases, they will increase at a different rate due to the polytropic compression which occurs, and temperature of the gases will increase as well. This leads us to the reason intercoolers are used prior to the air entering the engine's cylinders.

The turbine half of the compressor is where the exhaust gases are slowed, and kinetic energy is recovered through the interaction of the turbine and the gases. Due to the exhaust gas having a certain enthalpy, which is a measure of the available energy within itself, the work done to the turbine will be the change in enthalpy from the beginning of the turbine to the end of the turbine. The main things which effect the enthalpy of the gases in our situation is the exhaust gases velocity and temperature. The increase of exhaust gas velocity will increase it's kinetic energy, and in return will transfer more kinetic energy to the turbine when it is slowed. [I'm not quite sure how the exhaust temperature effects the turbine and the efficiency at which it runs]. This basically shows how the velocity of our turbine is proportionately effected by the velocity and temperature of exhaust gases.

The main benefits of turbochargers to modern cars now and in the future include: cheaper, lighter, faster, more reliable cars (can use smaller engine, more simple designs), cheaper transport costs (busses, trucks etc can use smaller engines), environmental impact (engine efficiency is improved, cleaner burning of air-fuel mixture), and more efficient use of fuel.

This is just a basic overview and I will go deeper into the topics, but could you explain to me again how the exhaust gas temperature effects the speed at which the turbine will spin? Is the temperature of the exhaust gas a factor which determines it's velocity as well?

Thanks,

12. May 3, 2015

### jack action

First, a naturally aspirated engine almost never reach 100% volumetric efficiency (typical is 75-95%), and when they do, it is only within a small rpm range (not necessarily at low rpm).

Also, it is not a problem per say. Volumetric efficiency uses the cylinder physical volume as a reference point, bu no law says that it as to be completely filled. An engine that has a 90% VE does not do a «better job» than one having a 75% VE. It can burn the fuel mixture just as well, giving similar fuel consumption and emissions. The real «problem» is that an engine with 75% VE will have to be larger to produce the same power as the one with 90% VE.

The advantage of superchargers (turbo or others) is that they turn faster than the engine so they can suck the same quantity of air while being smaller than an equivalent increase in engine size. Although they can be use to compensate for lost of VE like you mentioned.

I wouldn't say they are «key components». They are more of a safety feature. It is possible to make an engine without either of those components, if well balanced; But it is rarely done as it is easier to add a wastegate than trying to perfectly tune the compressor/turbine/engine combo.

The real advantage of turbocharger would be a better power-to-weight ratio (whether you want more power with the same engine weight or a lighter engine that produces the same power) due to the compressor and a better fuel efficiency due to the turbine recovering some energy. It is not cleaner: The environmental impact is if you use a lighter version to replace a bigger naturally aspirated engine, the weight reduction should affect the fuel consumption. It is not cheaper, more reliable or simpler; It is usually considered more complex which usually leads to more expensive and/or less reliable and/or more maintenance.

It is the ideal gas law again: Temperature increases, pressure increases so it can push harder on the turbine.

13. May 4, 2015

### Randy Beikmann

Vlad137, turbos aren't just used to increase an engine's breathing at high speeds. One of the nice features of turbo engines is the massive amount of torque they can produce at low speeds.
For a naturally aspirated engine (assuming no tuned intake or restriction, and intake valve closing at BDC), the cylinder pressure at wide-open-throttle is atmospheric. This is the limiting factor to torque.
Even at, say, 2000 RPM, you can cram a larger mass of air into the cylinder by pushing it in under a higher pressure than atmospheric. Compressing the air to 1.5 atmospheres allows putting 1.5 times as much air into the cylinder (assuming the inlet temperature is the same - intercooling?), and allowing a torque output of about 1.5 times as much.