Air Mass into Cylinder (Intake Charge)

[Jason Louison]

Hello Physics Forum Community! It sure has been a while! :) I have been hard at work on my goal; to create a spreadsheet that simulates the Internal Combustion Engine (Spark Ignition). I can't take all the credit for having come this far, so there will be links to a few sources below that I have used in my research. Here are some progress photos!

Sources:

“Home - Walter Scott, Jr. College of Engineering.” Home - Walter Scott, Jr. College of Engineering, www.engr.colostate.edu/~allan/thermo/page8/page8.html.

https://2k9meduettaxila.files.wordpress.com/2012/09/internal-combustion-engines-fundamentals-heywood.pdf

I have created a simulation method of my own for the mass of air entering and exiting the cylinder, but it is very simple. That being said, it probably has a lot of error associated with it. I have come to physics forums to see if there was a better alternative or suggestions of how I could improve the model.

The model is as follows: For any IC (Internal Combustion) SI (Spark Ignition) engine, there is an intake and exhaust valve opening and closing point, usually denoted in degrees BTDC, ABDC, ATDC, BBDC.

If we calculate the mass of air in the cylinder, for example, at t_ivo and t_ivc ,take the engine speed (rpm) and convert those values to time, we can derive an equation for mass flow rate with the linear slope formula:

dm/dt=(m₂—m₁)/(t_ivc—t_ivo)

Where m₂ is the total cylinder mass, (fuel and air), m₁ is the residual mass, t_ivc is the time at closing of intake valve, and t_ivo is the time at the opening of the intake valve. For the exhaust mass flow rate, just switch m₁ and m₂ and turn t_ivo and t_ivc into t_evo and t_evc

 

[Jason Louison]

Here are my current values for each variable:

 

[anorlunda]

dm/dt=(m2—m1)/(tivc—tivo)

What are you doing with dm/dt?

Your question isn't detailed enough to answer. I translate it as, "If I have the end points of a curve, can I approximate it with a straight line?" Sometimes yes, sometimes no. A sin wave is zero at the beginning and end of each cycle. It can be approximated by the constant zero. For some applications, zero is a good enough answer. For other applications not.

 

[Jason Louison]

What are you doing with dm/dt?

Your question isn't detailed enough to answer. I translate it as, "If I have the end points of a curve, can I approximate it with a straight line?" Sometimes yes, sometimes no. A sin wave is zero at the beginning and end of each cycle. It can be approximated by the constant zero. For some applications, zero is a good enough answer. For other applications not.

I am essentially using it as the slope of a linear equation for mass into the cylinder, as shown in this graph:

The reason why I am worried about this method is valve overlap. As you can clearly see in the example above, I have yet to come up with a solution to this. If I do dm/dt(overlap)=dm_intake—dm_exhaust, then the mass flow rate can be zero, and the equation would just state no air in entering nor leaving the cylinder. (Cylinder mass would be zero)

 

[anorlunda]

Your question is unanswerable as stated. To provide an answer, one would have to compare a linear assumption, with a more accurate first principles simulation. I mean first principles of physics. Or compare it with experiment. Compare it with something. You have nothing to compare it with.

In simulation, we call it verification and validation. Our trust in any simulation is low, or zero, until we have some way to compare its results to an independent source of data.

When we assume linearity in simulation, it usually applies to one of the coefficients of the equations. You seem to be going the other way assuming linearity in the results, not the coefficients. In my experience, that works <20% of the time. I speak of engineering where our purpose is to use the simulation to predict how the system behaves in scenarios we have not measured. In the computer gaming world, there can be a different approach to simulation based on appearances (like the end points of your lines). They might call that physics, but it isn't really. In any case, they consider their games successful.

So, if your purpose is to predict engine performance in different scenarios or with different parameters, I urge you to take a different approach, based on "first principles" of physics: Newton's laws, conservation of mass, energy, volume, momentum, thermodynamics, and so on.

On the other hand, if your purpose is to produce a spreadsheet that appears to behave like an engine, ignoring the physics, then I wish you success. But asking questions on a physics forum won't be very helpful.
'

 

[Jason Louison]

Your question is unanswerable as stated. To provide an answer, one would have to compare a linear assumption, with a more accurate first principles simulation. I mean first principles of physics. Or compare it with experiment. Compare it with something. You have nothing to compare it with.

In simulation, we call it verification and validation. Our trust in any simulation is low, or zero, until we have some way to compare its results to an independent source of data.

When we assume linearity in simulation, it usually applies to one of the coefficients of the equations. You seem to be going the other way assuming linearity in the results, not the coefficients. In my experience, that works <20% of the time. I speak of engineering where our purpose is to use the simulation to predict how the system behaves in scenarios we have not measured. In the computer gaming world, there can be a different approach to simulation based on appearances (like the end points of your lines). They might call that physics, but it isn't really. In any case, they consider their games successful.

So, if your purpose is to predict engine performance in different scenarios or with different parameters, I urge you to take a different approach, based on "first principles" of physics: Newton's laws, conservation of mass, energy, volume, momentum, thermodynamics, and so on.

On the other hand, if your purpose is to produce a spreadsheet that appears to behave like an engine, ignoring the physics, then I wish you success. But asking questions on a physics forum won't be very helpful.
'

Thank you for those wise words, anorlunda. I have decided to go for a compressible mass flow rate equation, given valve curtain area, discharge coefficient, pressure ratio, and temperature. This is as technical you can get with computer simulation (especially on a spreadsheet). I will make a brainstorming sheet right now.

 

[jack action]

If you want to really model the air flow, you will most likely need to factor in the intake and exhaust geometry.

From p. 208 of the book in your second link, you can find this important mention which can guide you in the right direction:

Due to the time-varying valve open area and cylinder volume, gas inertia effects, and wave propagation in the intake and exhaust systems, the pressures in the intake, the cylinder, and the exhaust during these gas exchange processes vary in a complicated way. Analytical calculation of these processes is difficult (see Secs. 7.6.2 and 14.3 for a review of available methods). In practice, these processes are often treated empirically using overall parameters such as volumetric efficiency to define intake and exhaust system performance.

This post might also help you understanding the phenomena of pressure waves and how their effects can be simplified.

 

[Jason Louison]

If you want to really model the air flow, you will most likely need to factor in the intake and exhaust geometry.

From p. 208 of the book in your second link, you can find this important mention which can guide you in the right direction:

This post might also help you understanding the phenomena of pressure waves and how their effects can be simplified.

Already on it!

 

[Jason Louison]

If you want to really model the air flow, you will most likely need to factor in the intake and exhaust geometry.

From p. 208 of the book in your second link, you can find this important mention which can guide you in the right direction:

This post might also help you understanding the phenomena of pressure waves and how their effects can be simplified.

Here's what I've got so far (Brainstorming Sheet):

The flow of air is choked, and reaches its maximum when it reaches the speed of sound. I decided to make a two zone model to especially highlight this phenomenon. Zone 1 is Subsonic Flow, whereas zone 2 is Supersonic (Critical/Choked) Flow.

ZONE ONE:

ZONE TWO:

*Note: A2 is the pressure ratio (x)